Then one can construct a model for the inverse limit by taking all the compatible sequences. This is a subspace of a product of compact spaces. This product is closed by Tychonoff …

This question was something I considered when looking into CW-structures on Grassmannians, but I found no general treatment of this in the literature: Question: Assume that $X$ is …

Given two infinite sets $A$, $B$ of natural numbers, write $A\preceq B$ if $B\setminus A$ is a finite set. Define the equivalence relation $A\sim B$ if $A\preceq B$ and $B\preceq A …

Suppose that $K$ is an $\textit{alternating}$ knot in $S^3$, and let $R_0$ be the space of homomorphisms from $\pi_1(S^3 - K)\to SU(2)$ which send meridians to trace free matrices. …

More specificaly, is there a haussdorf non-discrete topology on $\mathbb{Z}$ that makes it a topological group with the usual addition operation?

An arbitrary union, or a finite intersection, of open sets in a topological space is again open. What name is given to the hypothetical property that an arbitrary intersection of o …

What can be said about the relation between the complex and the real K-theory of a CW complex? An $n$-dimensional complex vector bundle is an $2n$-dimensional real vector bundle bu …

Is the universal covering of a connected open subset $U$ of ℝn diffeomorphic to an open subset of ℝn (standard differentiable structure)? If not true in general, is t …

Consider sequence $s(n) = \sin{nx}$. Are there values of $x$ for which the following holds: For every $y \in [-1,1]$ there is a subsequence of $s(n)$ converging to $y$? (Or perhaps …

I was wondering if anyone can suggest a reference which treats the Krull topology. Most of the books I have found don't go into any kind of detail. It is my understanding that the …

Hello. I have a question. Does there exist a continuous mapping $F:\mathbb{R}^2\rightarrow\mathbb{R}^2$ such that for every $c\in F(\mathbb{R}^2)$ there are two and only two po …

Suppose I have a continuous map $f:X\rightarrow Y$. Then one can wonder, whether for every open set $U\subset X$ the set $U':=\{x\in X|f^{-1}(f(x))\subset U\}$ is open again. This …

Suppose A and B are compact connected sets in the XY plane and XZ plane respectively in R^3. Suppose further that the the range of x-values taken by A and B are the same (i.e, proj …

Suppose a finite group $G$ acts on a standard probability space $(X, \mu)$ by measure-preserving actions (i.e. $\mu(g(A)) = \mu(A)$ for all $g \in G$ and $A \subset X$ measurable). …

What the title said. In a slightly more leisurely fashion:- Let $X$ be a compact, connected subset of $\mathbb{R}^2$ with more than one point, and let $x\in X$. Can $X\smalls …