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Results tagged with at.algebraic-topology
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user 5903
Homotopy theory, homological algebra, algebraic treatments of manifolds.
2
votes
Accepted
Approximations by compact sub-spaces
Q1. Consider the space of rationals $\mathbb{Q}$.
It is the direct limit of the family of finite unions of convergent sequences (including their limits), ordered by inclusion, as a set is closed iff i …
- 11.4k
6
votes
The Stone-Čech compactification of the fixed point set
Not without further assumptions.
First create an ordered space $X$ by identifying $\langle0,\omega_1\rangle$ and $\langle1,\omega_1\rangle$ in the product $2\times(\omega_1+1)$ to a point, $\Omega$ sa …
- 11.4k
1
vote
A question about local connectedness in metric spaces
No, examples abound, e.g., the $\sin\frac1x$-curve, i.e., the closure of
$\lbrace \sin\frac1x : 0 < x \le 1\rbrace$ in the plane. As noted below, this is not a good example (I misread the question).
…
- 11.4k