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that Tychonoff's theorem is complex - what does that mean? (Certainly it is always difficult to rigorously use the axiom of choice. But is this theorem harder...

it. By the way, everyone still does write "Tychonoff", including the wikipedia entry on Tychonoff's theorem (which by chance I rewrote, but not for linguistic...

Under Tychonoff's assumptions X is in fact normal: second-countable implies Lindelöf, and Lindelöf + regular implies normal (this is Tychonoff's lemma)...

invoke the finite intersection axiom, related to axiom of choice by Tychonoff's theorem; the relationship is not clear to me just right now. I guess this...

which is not necessary or appropriate—with the axiom of choice, Tychonoff's theorem is available. Planetmath gives a more reasonable proof. Dfeuer (talk)...

regular is the Tychonoff corkscrew. Red link, but OK. 67.198.37.16 (talk) 18:31, 26 November 2023 (UTC) The Tietze extension theorem can be applied to...

proving the results we state as Theorems 6.42, 6.47, and 6.48. Does anyone know about other sources supporting Tychonoff's precedence? If the claim is false...

however, was criticized for using the Axiom of Choice in the form of Tychonoff’s Theorem. Later, Henri Cartan proved the existence of invariant measures on...

2002 CSTAR 01:34, 21 Sep 2004 (UTC) The theorem is said to be "a direct application of the Tychonoff theorem". From this, I understand that one should...

for "gelfand" AND "naimark" AND "theorem" brings up many references to my theorem but no references to your theorem that don't also have the name "Segal"...

tell you its location, and I apologize again for that.) Of course, Tychonoff's theorem, and the fact that [ 0 , 1 ] ω {\displaystyle [0,1]^{\omega }} is...

compact Hausdorff space. Because Y is compact, the limit required for the theorem will exist. Because a compact Hausdorff space is regular, the condition...

for free. That's because the representation space is compact (by Tychonoff's theorem), so any closed set is compact. Then the continuous image of a closed...

This is a mistake. Moreover, this mistake reflects in the subsequent theorem, when it is proved that a compact space is net-compact. If the proof whose...

I know filters are very important. IMO the best looking proof of Tychonoff's theorem is using ultrafilters. But after reading the sections above me I...

parts of functional analysis rest? Tychonoffs theorem will definitly have to go and along with it many existence theorems in e.g. differential equations....

Kelley's book is also very famous, and he proved the theorem that AC is equivalent to Tychonoff's theorem. Articles on these people are certainly welcome and...

group is an restricted wreath product whereas the Universal Embedding Theorem (every extension of A by H is a subgroup of A Wr H) requires the unrestricted...

bounded. This is not a definition, this is the result of a theorem (the Heine-Borel theorem). I didn't read any farther in the article. I agree with a...