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From the Bay to LA.


Dec
8
awarded  Caucus
Dec
8
revised Without AC, it is consistent that there is a function with domain $\mathbb{R}$ whose range has cardinality strictly larger than that of $\mathbb{R}$?
added 44 characters in body
Dec
7
awarded  Scholar
Dec
7
accepted Without AC, it is consistent that there is a function with domain $\mathbb{R}$ whose range has cardinality strictly larger than that of $\mathbb{R}$?
Dec
7
comment Without AC, it is consistent that there is a function with domain $\mathbb{R}$ whose range has cardinality strictly larger than that of $\mathbb{R}$?
Pretty interesting, thanks Asaf.
Dec
7
comment Without AC, it is consistent that there is a function with domain $\mathbb{R}$ whose range has cardinality strictly larger than that of $\mathbb{R}$?
@BrianM.Scott Oops, thanks for clarifying that.
Dec
7
awarded  Student
Dec
7
asked Without AC, it is consistent that there is a function with domain $\mathbb{R}$ whose range has cardinality strictly larger than that of $\mathbb{R}$?
Dec
7
answered Number of non-isomorphic groups of order $p^2$
Dec
7
comment Number of non-isomorphic groups of order $p^2$
It's a bit of a sledgehammer here, but do you know the structure theorem for finitely generated abelian groups?
Dec
4
comment Prove that a $C^\infty$ vector field on $M$ can be extended to a $C^\infty$ vector field on $N$ .
When you say you have a smooth vector field $X$ on $M$, are you assuming that for each $p\in M$, there exists an open neighborhood $V$ of $p$ in $N$ and a vector field $\tilde{X}$ on $V$ which agrees with $X$ on $V\cap M$?
Nov
29
answered Conjugacy Class of a Group of Order 12
Nov
29
answered Finite field extensions and minimal polynomial
Nov
24
answered Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
Nov
24
revised $A$ and $A+y$ are homeomorphic where $A$ is open set
edited tags
Nov
23
comment Circle to circle homotopic to the constant map?
Are you asking for the existence of some $x$ such that $f(x)=-x$ or that $f(x)=-x$ for all $x$?
Nov
23
comment Circle to circle homotopic to the constant map?
What is $x$ in part (b)?
Nov
18
revised $S\subseteq V \Rightarrow \text{span}(S)\cong S^{00}$
fixed typo
Nov
14
revised Explicit description of a topology that proves $\mathbb{R}$ is not minimal Hausdorff.
edited title
Nov
2
comment Homotopy equivalence for $S^n$ with finite k punctures
The basic idea is to view $S^n\setminus\{k\text{ points}\}$ as a punctured sphere with $k-1$ other missing points. By stereographic projection (there are known formulas for this), this is homotopy equivalent to $\mathbb{R}^n$ minus $k-1$ points. The punctured plane is then homotopy equivalent to the wedge of $k-1$ copies of $S^{n-1}$. Geometrically, fix some base point, and then draw $k-1$ loops out from this point that encircle exactly one of the missing points. The rest of $\mathbb{R}^n$ deformation retracts onto these loops, and this is equivalent to the wedge sum.