Ben Steffan
  • Member for 2 years, 7 months
  • Last seen more than 1 year ago
Some confusion regarding a quotient space: what is the space $\mathbb{S}^1\times I/ \mathbb{S}^1\times \{1\}$?
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3 votes

Often in topology, one takes quotients by a subspace; this just means taking all the points in the subspace and identifying them to a single point. In your definition, this means $X / Y$ where $Y \...

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Prove that a subset is open relative to another subset (Proof Verification)
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1 votes

The proof is correct, but it seems a bit too wordy to me. I'd shorten the first part of your proof to Suppose $E$ is open relative to $Y$. Then, for each $e \in E$, there is some $r_e \in \mathbb{...

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Invertibility of elements in $A[x]$ with coefficients in the Jacobson radical
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2 votes

It does not have to be the case that $\mathfrak{R}((x) + \cdots + (x^n))$ is finite, so Nakayama is not applicable here in general. There is a second, much more serious error, however: for the ...

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Faces of a simplex in a simplicial complex is in the simplicial complex
1 votes

Take $K = \{\{a, b, c\}\}$. Condition 2 is trivially satisfied, since there is only a single element in $K$. However, condition 1 is not satisfied: For instance we have that $\{a\} \subset \{a, b, c\}$...

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In an algebraic system, is there a general name for an element that behaves like 0 does for multiplication in $\mathbb R$?
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2 votes

Yes, such an element is known as an absorbing element.

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Brouwer's theorem proof using Category theory
2 votes

To answer your first question: yes, of course. If you go back to the definition of category, there is nothing saying that objects in a category need to be of the same type, whatever that might mean. ...

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Homology of spheres: how to show that $\tilde{H}_{n-1}(S^{n-1})\cong\tilde{H}_{n}(S^{n})$, without Mayer Vietoris
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2 votes

Consider $S^n$ to be the suspension $\Sigma S^{n - 1}$ for all $n \geq 1$. Let $C^n_+$ and $C^n_-$ denote the upper and lower cone of $\Sigma S^{n - 1}$, respectively, and let $S^{n - 1} \subseteq \...

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Euler characteristic of projective plane (rank$(H_1(RP^2))=$ rank$(Z_2)=0?$)
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3 votes

The rank of a module $M$ is the rank of its free part, or equivalently the maximal number of linearly independent elements in $M$. $\mathbb{Z}_2$ has no linearly independent elements, since $2 \cdot 1 ...

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