Ben Steffan
• Member for 2 years, 7 months
• Last seen more than 1 year ago

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 $Y \... View answer Accepted answer 1 votes The proof is correct, but it seems a bit too wordy to me. I'd shorten the first part of your proof to Suppose$E$is open relative to$Y$. Then, for each$e \in E$, there is some$r_e \in \mathbb{...

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 ...

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 $\{a\} \subset \{a, b, c\}$...

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

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 $S^{n - 1} \subseteq \... View answer Accepted answer 3 votes The rank of a module$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 ...