bio | website | |
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age | 24 | |
visits | member for | 4 years, 6 months |
seen | 1 hour ago | |
stats | profile views | 10,586 |
Apr 17 |
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Homology of infinite intersection
It seems like pretty much any interesting construction where the intersection isn't a finite CW-complex is likely to be a counterexample. For instance, the standard construction of the Cantor set by deleting intervals is a counterexample (more simply, an analogous construction of $\{0,1,1/2,1/3,1/4,\dots\}$ by deleting intervals from $[0,1]$ also works). One more promising definition of "nice" would be that both the $X_n$ and the intersection are all finite CW-complexes; I haven't been able to come up with a counterexample to that. |
Apr 16 |
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First-countable topological monoids without local absorbing elements whose topology is induced by a semimetric
Also, you really want to assume that the topology is semimetrizable, not just that it is first-countable (I don't know whether these are equivalent, but I doubt they are). Chris's construction is quite flexible and can easily be modified to be "resilient". For instance, you could take $X\coprod\mathbb{N}$, where adding elements of $X$ to anything but $0$ is the same as adding $1$. |
Apr 16 |
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First-countable topological monoids without local absorbing elements whose topology is induced by a semimetric
A monoid is resilient iff it has no idempotents besides the identity, since any idempotent $i$ is absorbing in the submonoid $\{1,i\}$ and any (locally) absorbing element is idempotent. |
Apr 16 |
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If $(\mathbb M, \tau)$ is a topological monoid, is $\tau$ always induced by a [left] subinvariant semimetric?
Chris is not saying that any topology on $M$ makes it a topological monoid, but that any topology on $X$ makes $M=X\coprod \{0,\infty\}$ a topological monoid. If I'm not mistaken, though, any semimetric on $X$ can be extended to a subinvariant semimetric on $M$ (just make $0$ and $\infty$ infinitely far away from $X$ and each other), so this will only give a counterexample in the case that $X$ is not semimetrizable at all. |
Apr 16 |
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If $(\mathbb M, \tau)$ is a topological monoid, is $\tau$ always induced by a [left] subinvariant semimetric?
No need to apologize for answering your own question; it is the correct thing to do if you learn an answer later! |
Apr 15 |
reviewed | Reject suggested edit on nontrivial theorems with trivial proofs |
Apr 15 |
reviewed | Reject suggested edit on nontrivial theorems with trivial proofs |
Apr 15 |
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Simple groups and words
More generally, take anything in the normal subgroup of $F$ generated by $n$th powers. |
Apr 13 |
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If $(\mathbb M, \tau)$ is a topological monoid, is $\tau$ always induced by a [left] subinvariant semimetric?
To elaborate on my last comment, every poset with the Alexandrov topology is canonically semimetrizable (let $d(x,y)=0$ if $x\leq y$ and $d(x,y)=1$ otherwise). Incidentally, every semilattice is also a topological monoid and this semimetric is subinvariant. |
Apr 13 |
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If $(\mathbb M, \tau)$ is a topological monoid, is $\tau$ always induced by a [left] subinvariant semimetric?
Do you know of a characterization of what spaces admit any semimetric structure at all? If I'm not mistaken, these are a lot more general than metrizable spaces, since the possibility of having $d(x,y)=0$ but $d(y,x)>0$ lets you get interesting non-Hausdorff topologies. |
Apr 11 |
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When does topological homogeneity imply algebraic homogeneity? Pseudo-arc and Hilbert cube
There are certainly quotients of compact groups that have the fixed point property (for instance, even-dimensional projective spaces). |
Apr 7 |
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Is the space of *-homomorphisms between two $C^*$-algebras locally path connected
You don't actually need $A$ to be commutative, because when $B$ is commutative all homomorphisms from $A$ to $B$ will factor through the Gelfand transform of $A$. |
Apr 7 |
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Is the space of *-homomorphisms between two $C^*$-algebras locally path connected
I believe your argument works when $B$ is commutative, but I don't see why it works when only $A$ is commutative. If the image of $A\to B$ is not central, then you may be able to conjugate it by a continuous family of unitaries to get a nontrivial path in $\mathrm{Hom}(A,B)$. |
Apr 2 |
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Is every Noetherian Commutative Ring a quotient of a Noetherian Domain?
Very nice! I am reminded of a similar cardinality constraint I found in this answer. |
Apr 2 |
answered | Compactly supported cohomology of homotopy equivalent manifolds |
Mar 30 |
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Given a 2-category, is the hammock localization wrt the equivalences equivalent to taking the hom-wise nerve of the maximal subgroupoids?
If $C$ has one object and one 1-morphism, the first construction forgets about all the 2-morphisms but the second does not. |
Mar 27 |
reviewed | Reject suggested edit on Which Lie groups have adjoint representations that are bounded away from zero? |
Mar 26 |
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Automorphism group of compact abelian group
By Pontryagin duality, $X$ has the same automorphisms as its character group, which is discrete. In particular, for instance, the automorphisms of a torus are just $GL_n(\mathbb{Z})$. |
Mar 25 |
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Are there models for homotopy colimits and limits of simplicial sets that generalize Kan's suspension and loop functors?
The Kan loop group also has the advantage of actually being a simplicial group on the nose, rather than up to homotopy. On your related question, there is an unpointed version of the Kan loop group due to Dwyer and Kan. |
Mar 25 |
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Why doesn't choice imply global choice (in NBG)?
I think this is a fine question, but it's basically the same as this question that was migrated a few days ago. |