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two queens
mathematics and death
not cheerful not sad
guide me through the land
pat me on my head
they live
in my one man nation
i follow them
to my destination
wh,
(long ago)
polynomials over finite Galois field
spread so evenly across their finite affine space
i wish for a network of friends
to count on
wh,
19960305/06
8h

comment 
Is there a homology theory that gives a *necessary and sufficient* condition for homotopy equivalence?
Homology is algorithmic while homotopy is not. At least that's the idea. 
15h

revised 
Topological razors (balllike spaces)
an ommision put back 
22h

comment 
Firstcountable topological monoids without local absorbing elements whose topology is induced by a semimetric
I don't see you mentioning $1$ (or $e$). Do you consider monoids or semigroups? 
22h

revised 
Topological razors (balllike spaces)
a significant correction 
1d

comment 
Knaster Tarski theorem, example needed
Sure. Elegant! After all, it was Stefan Banach himself. 
1d

answered  Topological razors (balllike spaces) 
2d

comment 
Generalization of notion of convexity
Consider any finite $\ X\subset \mathbb R^2.\ $ Then according to your definition, $\ X\ $ is $r$convex, right? Also $\ \mathbb Q^2\ $ is $r$convex, etc. 
2d

comment 
Prove that (AxB)∩(CxD)=(A∩C)x(B∩D)
Perhaps this is the simplest question asked at MO at any time so far. 
2d

awarded  Promoter 
2d

comment 
Dimension of a set detected by a homology class
@Igor Belegradek (quote: search the web on "pseudocircle" and "continuum")no need to. But thank you for your effort. 
2d

comment 
Dimension of a set detected by a homology class
Anton, your link says "pseudocircle", while it points to wikipedia article on pseudoarc, and it does not mention pseudocircle at all. Could you comment about it? 
2d

comment 
Dimension of a set detected by a homology class
Anton, what do you mean by statement: For sure you can not expect a subset homeomorphic to $\mathbb R^p$ ? 
Apr 18 
comment 
Dimension of a set detected by a homology class
First there was the absolute (just for the spaces, not for subsets) Poincare duality theorem. Then there was AlexanderPontryagin theorem for subsets of a manifold. On the later occasion Pontryagin introduced his duality theorem for topological groupsinitially it was about compact abelian groups versus discrete abelian groups. (This was generalized to locallyt compact abelian groups Egbert van Kampen in 1935 and André Weil in 1940see wikipedia). An early result about dissecting $\mathbb R^n$ by a compact subset was obtained by Karol Borsuk. Etc. (you need to ask not me but a specialist). 
Apr 18 
comment 
Dimension of a set detected by a homology class
That's what the topological duality theorems are about. 
Apr 18 
revised 
Homology of infinite intersection
order of words (a typo) 
Apr 17 
comment 
Homology of infinite intersection
Let me make the above complete. Consider the category of hpairs $\ (X\ A).\ $ These are pairs homotopically dominated (as pairs) by finite polyhedral pairs. Then this category admits exactly one ES homology/cohomology theory (JK suggested to me to publish it in 1970/71). Here, in this topic, we still need to narrow the class of spaces to ANRs to get answer YES because of the behavior of the inverse limit. 
Apr 17 
comment 
Homology of infinite intersection
Just in case, and for the sake of this topic, I'd like to stress quietly that when we talk about nice compact spaces, meaning ANRs, then all ES homology/cohomology theories are equivalent. 
Apr 17 
comment 
Homology of infinite intersection
*** hm, ... *** 
Apr 17 
answered  Homology of infinite intersection 
Apr 17 
answered  Homology of infinite intersection 