Let $(X,A)$ and $(Y,B)$ be pairs of spaces and subspaces, let $\operatorname{Map}(X,Y)$ the space of maps $f:X\to Y$ equipped with the compact-open topology and let $\operatorname{ …

For $n\geq 2$ let $(S^n,p)$ be the $n$-sphere with a base point $p$. Let $1:S^n\to S^n$ denote the identity map. Let us define the map $Wh_1: \pi_i(S^n,p)\to \pi_{i+n-1}(S^n,p), …

Consider the following claim: Let $p:M \to N$ be a (surjective) submersion of finite-dimensional smooth manifolds. Let $J$ denote one of $[0,1],\ [0,1),\ (0,1]$. Then $p_*:M …

I would be very grateful for any information or pointers for the following: 1) Fix an open subset $U$ of $\mathbb{CP}^1$. a) Does the set of all holomorphic maps from $U$ to $\mat …

I've coded up the FFT for a dataset I'm working with. My intent is to create a waterfall plot of the result, but the problem I'm running into is if I change my input data size, the …

Hi, $ SU ( 1 )$ has a well-known mapping to $S_{1}$ $ SU ( 2 )$ almost has a isomorphism mapping to $S_{2}$; actually to a double cover of $S_{2}$ is there a known topological m …

Suppose $A$ is an abelian torsion group, with no elements of order $p$, and let $P$ be an abelian $p$-group (i.e., the order of each element is a power of $p$). It sure seems to m …

Let $X$ and $Y$ be CW complexes. Inside of the space of maps $\mathrm{map}(X,Y)$, we have the subspace $\mathrm{CW}(X,Y)$, consisting of just the cellular maps from $X$ to $Y$. T …

Let $G$ and $H$ be torsion abelian groups. Are the following are equivalent: $\mathrm{Hom}(G, H) = 0$ $\mathrm{map}_*( K(G, m), K(H,n)) \sim *$ for all $n, m\geq 1$ ? Clearly …