Wlodzimierz Holsztynski

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1,573 reputation
719
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location sqrt(-1)
age
visits member for 3 years, 8 months
seen 8 hours ago
 
  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,
1996-03-05/06



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 (ball-like spaces)
an ommision put back
22h
comment First-countable 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 (ball-like spaces)
a significant correction
1d
comment Knaster Tarski theorem, example needed
Sure. Elegant! After all, it was Stefan Banach himself.
1d
answered Topological razors (ball-like 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 "pseudo-circle" 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 "pseudo-circle", while it points to wikipedia article on pseudo-arc, and it does not mention pseudo-circle 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 Alexander-Pontryagin theorem for subsets of a manifold. On the later occasion Pontryagin introduced his duality theorem for topological groups--initially 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 1940--see 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 h-pairs $\ (X\ A).\ $ These are pairs homotopically dominated (as pairs) by finite polyhedral pairs. Then this category admits exactly one E-S 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 ANR-s 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 ANR-s, then all E-S 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