Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with general-topology
Search options not deleted
user 460691
Everything involving general topological spaces: generation and description of topologies; open and closed sets, neighborhoods; interior, closure; connectedness; compactness; separation axioms; bases; convergence: sequences, nets and filters; continuous functions; compactifications; function spaces; etc. Please use the more specific tags, (algebraic-topology), (differential-topology), (metric-spaces), (functional-analysis) whenever appropriate.
2
votes
Accepted
"Unfolding" a higher genus surface
While your question is a bit imprecise (which is fine!), the answer is more or less yes. The idea is to generalize the "coordinates" on the torus given by the unit square. Here is a picture from Hatch …
- 2,625
4
votes
Accepted
A torus whose middle is tied in an overhand knot; how many holes does it have?
The surface in the picture is still a torus, even though it is twisted in the middle. We can still define a homeomorphism from the torus to the surface in the picture, for instance by using the coordi …
- 2,625
0
votes
0
answers
23
views
Is the covering image of a graph a graph?
Suppose $X$ is a graph (a $1$-dimensional CW complex), and $X \to Y$ is a covering map. Then is $Y$ a graph?
I think the answer is yes, but I haven't been able to think of a proof.
Edit: After posting …
- 2,625
0
votes
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
Here is one solution to this exercise, which relies only on a few key insights. Below, $X$ and $Y$ are topological spaces, and $S \subseteq X$.
First, consider the inclusion map $i: S \to X$, which is …
- 2,625
7
votes
Accepted
How can I show that circle does not have the same homotopy type as any finite space?
If $X$ is a finite space and $f : S^1 \to X$ is a homotopy equivalence with homotopy inverse $g : X \to S^1$, then the map $g \circ f : S^1 \to S^1$ must be homotopic to the identity. But by degree th …
- 2,625
5
votes
1
answer
104
views
Are these normed vector spaces homeomorphic?
Let $X = \{(x_n) \mid \sum_{n = 1}^\infty |x_n| < \infty\}$, and let $\|\cdot\|_1$ and $\|\cdot\|_\infty$ be the $L^1$ and $L^\infty$ norms on $X$, respectively. Are the normed vector spaces $(X, \|\c …
- 2,625