• Log InLog In
  • Register
Liquid`
Team Liquid Liquipedia
EDT 23:38
CEST 05:38
KST 12:38
  • Home
  • Forum
  • Calendar
  • Streams
  • Liquipedia
  • Features
  • Store
  • EPT
  • TL+
  • StarCraft 2
  • Brood War
  • Smash
  • Heroes
  • Counter-Strike
  • Overwatch
  • Liquibet
  • Fantasy StarCraft
  • TLPD
  • StarCraft 2
  • Brood War
  • Blogs
Forum Sidebar
Events/Features
News
Featured News
[ASL21] Ro16 Preview Pt2: All Star10Team Liquid Map Contest #22 - The Finalists16[ASL21] Ro16 Preview Pt1: Fresh Flow9[ASL21] Ro24 Preview Pt2: News Flash10[ASL21] Ro24 Preview Pt1: New Chaos0
Community News
2026 GSL Season 1 Qualifiers19Maestros of the Game 2 announced92026 GSL Tour plans announced15Weekly Cups (April 6-12): herO doubles, "Villains" prevail1MaNa leaves Team Liquid25
StarCraft 2
General
MaNa leaves Team Liquid Maestros of the Game 2 announced 2026 GSL Tour plans announced Team Liquid Map Contest #22 - The Finalists Blizzard Classic Cup @ BlizzCon 2026 - $100k prize pool
Tourneys
2026 GSL Season 1 Qualifiers INu's Battles#14 <BO.9 2Matches> Sparkling Tuna Cup - Weekly Open Tournament GSL CK: More events planned pending crowdfunding RSL Revival: Season 5 - Qualifiers and Main Event
Strategy
Custom Maps
[D]RTS in all its shapes and glory <3 [A] Nemrods 1/4 players [M] (2) Frigid Storage
External Content
Mutation # 522 Flip My Base The PondCast: SC2 News & Results Mutation # 521 Memorable Boss Mutation # 520 Moving Fees
Brood War
General
ASL21 General Discussion Leta's ASL S21 Ro.16 review BW General Discussion BGH Auto Balance -> http://bghmmr.eu/ Data needed
Tourneys
[Megathread] Daily Proleagues Escore Tournament StarCraft Season 2 [ASL21] Ro16 Group C [ASL21] Ro16 Group D
Strategy
Simple Questions, Simple Answers What's the deal with APM & what's its true value Any training maps people recommend? Fighting Spirit mining rates
Other Games
General Games
Nintendo Switch Thread Dawn of War IV Diablo IV Total Annihilation Server - TAForever Starcraft Tabletop Miniature Game
Dota 2
The Story of Wings Gaming
League of Legends
G2 just beat GenG in First stand
Heroes of the Storm
Simple Questions, Simple Answers Heroes of the Storm 2.0
Hearthstone
Deck construction bug Heroes of StarCraft mini-set
TL Mafia
Vanilla Mini Mafia Mafia Game Mode Feedback/Ideas TL Mafia Community Thread Five o'clock TL Mafia
Community
General
US Politics Mega-thread Canadian Politics Mega-thread Things Aren’t Peaceful in Palestine Russo-Ukrainian War Thread YouTube Thread
Fan Clubs
The IdrA Fan Club
Media & Entertainment
[Manga] One Piece Anime Discussion Thread [Req][Books] Good Fantasy/SciFi books Movie Discussion!
Sports
2024 - 2026 Football Thread Formula 1 Discussion McBoner: A hockey love story Cricket [SPORT]
World Cup 2022
Tech Support
Strange computer issues (software) [G] How to Block Livestream Ads
TL Community
The Automated Ban List
Blogs
Sexual Health Of Gamers
TrAiDoS
lurker extra damage testi…
StaticNine
Broowar part 2
qwaykee
Funny Nicknames
LUCKY_NOOB
Iranian anarchists: organize…
XenOsky
Customize Sidebar...

Website Feedback

Closed Threads



Active: 1983 users

Filters in Topology

Blogs > Plexa
Post a Reply
1 2 Next All
Plexa
Profile Blog Joined October 2005
Aotearoa39261 Posts
December 16 2010 19:13 GMT
#1
For those of you who don't know, I'm currently studying for my Honours in Mathematics. Part of that comprises a dissertation we have to write on a research topic (not necessarily new research). For my project I am working in an area of Topology which deals with Convergence Spaces (it's like a generalised topological space).

I am currently in the process of writing up the work I have done over the last semester (it is a two semester project, one semester remaining to finish it!). After about a week of slugging away at things, I have finally produced the first draft of the first section of my dissertation - and well, it feels damn good !

As with everything in my life, I thought I would share it with TL for those few people that might be remotely interested.

This section of my dissertation concerns Filters. They are a kind of generalised sequence in arbitrary topological spaces. They are the fundamental object of a convergence space and hence studying them in a topological setting is necessary before proceeding into the more general setting of a convergence space. There are three parts to this section: the first part concerns general definitions and some key results, the second concerns an application to the Riemann Integral and the last concerns an application to compactness (with the slickest proof of tychonoff's theorem on the product of compact topological spaces you can find!)

Some general notes:
- The introductory paragraphs to each section will be getting rewrites
- There is one proof in the integration section which appeals to a theorem not proven in the paper, it is noted and I should probably include the theorem
- If you spot any errors please let me know latex can be a bitch some times!

Link: http://www.teamliquid.net/staff/Plexa/Dissertation/filters.pdf

Enjoy!

Administrator~ Spirit will set you free ~
Bibbit
Profile Blog Joined December 2009
Canada5377 Posts
December 16 2010 19:19 GMT
#2
I would read it because I've always got the impression that you're a really smart guy but I wouldnt understand anything. Math has always frightened me.

But best of luck with your dissertation though. :D:D:D
wherebugsgo
Profile Blog Joined February 2010
Japan10647 Posts
December 16 2010 19:53 GMT
#3
Haha, I'm taking the honors introduction to analysis course here at Berkeley, and we covered filters a month or so ago. Tomorrow is our final >_<

http://math.berkeley.edu/~wodzicki/H104.F10/Topology.pdf

Filters start on page 4, but you already know all of this stuff.

Good luck with your dissertation!
Plexa
Profile Blog Joined October 2005
Aotearoa39261 Posts
December 16 2010 19:58 GMT
#4
Ah gl for your final! You must have covered nets as well I fortunately got to skip all of that haha
Administrator~ Spirit will set you free ~
vAltyR
Profile Blog Joined July 2008
United States581 Posts
December 16 2010 19:58 GMT
#5
Very interesting. I wish I understood it. I don't know very much about topology, so most of this feels way over my head, even as a math major myself. The LaTeX looks fine though, from what I can tell.
내 호버크라프트는 장어로 가득 차 있어요
vvSiegvv
Profile Joined March 2010
United States364 Posts
December 16 2010 20:32 GMT
#6
Wish I could understand this, but I haven't gotten into topology at all yet, but it sounds pretty interesting. (2nd year math/compsci major)

Best of luck Plexa!
EsbenPM
Profile Joined April 2006
Denmark364 Posts
December 16 2010 20:35 GMT
#7
Looks interesting although i don't really understand much of it. But good luck anyway on your future work.

Oh, and making that look good in Latex must have been a pain in the ass with all those special characters and math expressions
Hi
LightRailCoyote
Profile Blog Joined January 2008
United States982 Posts
December 16 2010 20:36 GMT
#8
going to read it now.
AKA SurfSolar ----- This is the product of a DIY inadequate home
micronesia
Profile Blog Joined July 2006
United States24770 Posts
December 16 2010 20:47 GMT
#9
I'm not exactly sure what an Honours in Mathematics is equivalent to in the systems I'm familiar with. After you finish your dissertation, what will that make you?

I'd give you feedback but I'm too unfamiliar with this type of math to be much help.
ModeratorThere are animal crackers for people and there are people crackers for animals.
PrinceXizor
Profile Blog Joined April 2010
United States17713 Posts
Last Edited: 2010-12-16 22:07:21
December 16 2010 22:05 GMT
#10
Now i may be an english major, but i've got to tell you there apparently is an error in the first sentence:
It quickly becomes apparent that sequences are not adequet in a general topo-
logical setting and that new more general concepts need to be introduced.

Adaquate is spelled wrong, and the latter half: "and that new more general concepts need to be introduced." should either have the e in new changed to now, or have a comma after new.

"and that new, more general concepts need to be introduced".

But all of the math gibberish seems very intelligent. :D i noticed a few more errors that may or may not be errors depending on gibberish context. are you in the proofreading stage yet?

EDIT: and also this is a rather dull and confusing beginning for the paper anyway. perhaps explain what makes it apparent, something like "Upon using some gibberish with another thing, it becomes apparent..." ect.
Pokebunny
Profile Blog Joined June 2008
United States10654 Posts
December 16 2010 22:55 GMT
#11
I thought it was adequate, not adaquate.
Semipro Terran player | Pokebunny#1710 | twitter.com/Pokebunny | twitch.tv/Pokebunny | facebook.com/PokebunnySC
PrinceXizor
Profile Blog Joined April 2010
United States17713 Posts
December 16 2010 23:02 GMT
#12
On December 17 2010 07:55 Pokebunny wrote:
I thought it was adequate, not adaquate.

it is. epic fail by me. my bad.
Laconic
Profile Joined June 2010
United States32 Posts
Last Edited: 2010-12-16 23:07:27
December 16 2010 23:07 GMT
#13
Muphry's Law is inerrant.

And wow, nice job, Plexa. I don't even begin to understand what you are writing about, but I am impressed! It is like some sort of mysterious, majestic poetry written by Martians.
blahman3344
Profile Blog Joined March 2009
United States2015 Posts
Last Edited: 2010-12-16 23:29:39
December 16 2010 23:28 GMT
#14
I was able to understand it (with my inferior math knowledge) until the basic concepts part, so I'd say that you did a good job writing your draft. =)
Though I have to say, if that first part is really that long, I can only imagine how long the rest of the dissertation is going to be. ^^

well good luck Plexa, I'm sure you'll do fine. =P
I like haikus and / I can not lie. You other / brothers can't deny
]343[
Profile Blog Joined May 2008
United States10328 Posts
December 17 2010 00:02 GMT
#15
Hmm, about math writing:

Please end your sentences with periods! Even statements of "remarks"/"lemmas" etc.. (and equations are sentences (or parts thereof) too, so if they end a sentence, use a period!" (You end sentences with periods like... half the time.) [E.g. Lemma 1.44 should have a period after the (IV). -L(f,P) = U(-f,P). And perhaps commas after the other equations.]

You could also try to use the \begin{eqnarray} environment for that, though I suppose that's been deprecated... rather, use the \begin{align} environment. This gives you equation numbers on each line (after the equation, though... so if you want the number to go before the equation, just stick with this. And maybe use \textrm to make it non-math-mode.) Automatically numbered equations
can be annoying to keep up with, but you can do like \label and \ref and funny things like that to keep track of it dynamically (it requires compiling twice though.)

Try not to form run-on sentences. Use commas or semicolons (or even periods) as necessary. (As a general rule, if the sentence has more than one clause, it should have a comma or semicolon!) Also, fix typos. For example, Remark 1.49: "havenn't." Also in Remark 1.49, "implicitly" would be better than "silently," I feel.

Too bad I don't understand all the math itself though ... maybe I'll take topology in a year or two though, so yay
Writer
Plexa
Profile Blog Joined October 2005
Aotearoa39261 Posts
December 17 2010 02:04 GMT
#16
Thanks very much for all of that ]343[, I'm not going to touch this thing today since it would be terrible for my sanity, but when I get to reviewing it tomorrow or next week I'll incorporate the things you suggest.
On December 17 2010 05:47 micronesia wrote:
I'm not exactly sure what an Honours in Mathematics is equivalent to in the systems I'm familiar with. After you finish your dissertation, what will that make you?
At the moment I have a Bsc in Maths, after I'm done with this year I'll have a Bsc (hons) in Maths. The honours year comprises of 6 papers and 1 year long dissertation. It's not expected to be groundbreaking or revolutionary in anyway, it's purely for the research experience. After this I will most likely begin my Masters (that would be in july next year) and then go from there.
Administrator~ Spirit will set you free ~
micronesia
Profile Blog Joined July 2006
United States24770 Posts
December 17 2010 02:10 GMT
#17
Okay that makes a bit more sense. I was looking through and this document is pretty dense but not substantive enough to be the type of dissertation that would get you a doctorate :p
ModeratorThere are animal crackers for people and there are people crackers for animals.
Plexa
Profile Blog Joined October 2005
Aotearoa39261 Posts
December 17 2010 02:53 GMT
#18
Yeah this is the baby stuff anyway, all background information haha
Administrator~ Spirit will set you free ~
See.Blue
Profile Blog Joined October 2008
United States2673 Posts
December 17 2010 03:17 GMT
#19
Putting off studying for my analysis final as well and saw this haha. Latex makes everything look so pretty. Great job so far!
Klockan3
Profile Blog Joined July 2007
Sweden2866 Posts
Last Edited: 2010-12-17 04:00:14
December 17 2010 03:59 GMT
#20
F.3 is wrong, it should be "then" and not "and".
1 2 Next All
Please log in or register to reply.
Live Events Refresh
BSL
19:00
RO16 TieBreaker - Group A
LiquipediaDiscussion
[ Submit Event ]
Live Streams
Refresh
StarCraft 2
RuFF_SC2 212
ProTech27
StarCraft: Brood War
ggaemo 90
Nal_rA 42
NaDa 28
Icarus 3
910 1
Dota 2
NeuroSwarm507
ROOTCatZ5
LuMiX0
League of Legends
JimRising 710
Super Smash Bros
Mew2King282
Heroes of the Storm
Khaldor184
Other Games
summit1g10319
Fnx 1033
WinterStarcraft343
ViBE147
amsayoshi46
kaitlyn39
Organizations
Other Games
gamesdonequick1098
BasetradeTV185
StarCraft 2
Blizzard YouTube
StarCraft: Brood War
BSLTrovo
[ Show 14 non-featured ]
StarCraft 2
• Sammyuel 26
• AfreecaTV YouTube
• intothetv
• Kozan
• IndyKCrew
• LaughNgamezSOOP
• Migwel
• sooper7s
StarCraft: Brood War
• RayReign 62
• BSLYoutube
• STPLYoutube
• ZZZeroYoutube
League of Legends
• Lourlo1027
Other Games
• Scarra2180
Upcoming Events
Sparkling Tuna Cup
6h 22m
WardiTV Map Contest Tou…
7h 22m
MaxPax vs SHIN
Clem vs Classic
Ladder Legends
11h 22m
Solar vs GgMaChine
Bunny vs Cham
ByuN vs MaxPax
BSL
15h 22m
CranKy Ducklings
20h 22m
Replay Cast
1d 5h
Wardi Open
1d 6h
Afreeca Starleague
1d 6h
Soma vs hero
Monday Night Weeklies
1d 12h
Replay Cast
1d 20h
[ Show More ]
Replay Cast
2 days
Afreeca Starleague
2 days
Leta vs YSC
Replay Cast
3 days
The PondCast
4 days
KCM Race Survival
4 days
Replay Cast
4 days
Replay Cast
5 days
Escore
5 days
Replay Cast
5 days
Replay Cast
6 days
IPSL
6 days
Ret vs Art_Of_Turtle
Radley vs TBD
BSL
6 days
Replay Cast
6 days
Liquipedia Results

Completed

Escore Tournament S2: W4
RSL Revival: Season 4
NationLESS Cup

Ongoing

BSL Season 22
ASL Season 21
CSL 2026 SPRING (S20)
IPSL Spring 2026
KCM Race Survival 2026 Season 2
StarCraft2 Community Team League 2026 Spring
WardiTV TLMC #16
Nations Cup 2026
IEM Rio 2026
PGL Bucharest 2026
Stake Ranked Episode 1
BLAST Open Spring 2026
ESL Pro League S23 Finals
ESL Pro League S23 Stage 1&2
PGL Cluj-Napoca 2026

Upcoming

Escore Tournament S2: W5
Acropolis #4
BSL 22 Non-Korean Championship
CSLAN 4
Kung Fu Cup 2026 Grand Finals
HSC XXIX
uThermal 2v2 2026 Main Event
Maestros of the Game 2
2026 GSL S2
RSL Revival: Season 5
2026 GSL S1
XSE Pro League 2026
IEM Cologne Major 2026
Stake Ranked Episode 2
CS Asia Championships 2026
IEM Atlanta 2026
Asian Champions League 2026
PGL Astana 2026
BLAST Rivals Spring 2026
TLPD

1. ByuN
2. TY
3. Dark
4. Solar
5. Stats
6. Nerchio
7. sOs
8. soO
9. INnoVation
10. Elazer
1. Rain
2. Flash
3. EffOrt
4. Last
5. Bisu
6. Soulkey
7. Mini
8. Sharp
Sidebar Settings...

Advertising | Privacy Policy | Terms Of Use | Contact Us

Original banner artwork: Jim Warren
The contents of this webpage are copyright © 2026 TLnet. All Rights Reserved.