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Results tagged with gn.general-topology
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user 90655
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
4
votes
1
answer
570
views
A question on Möbius strip and Jordan curve
If $A\subset \Bbb R^2$ then is the following statement true?
$\{(x,y)\in {(A\times A)/ \sim}\,\,\,|\,\, (x,y)\sim(y,x)\}\simeq$ Möbius strip $\iff A$ is a Jordan curve.
- 4,195
2
votes
0
answers
132
views
Example of compact fiber bundle with noncompact fibers
This is a cross post of MSE post somehow:
Is there any example of compact fiber bundle $E$ with noncompact fibers $F$?
Obviously if the base space $B$ is $T_1$ then there is no such example.
- 4,195
3
votes
2
answers
408
views
A question on continuous maps from Möbius to itself
Let $M$ denotes the Möbius strip. Then is it true that
For every continuous map $f:M\to M$ there is $x\in M^\circ$ ($x\notin\partial M$) such that $f(f(x))=x$?
- 4,195
0
votes
1
answer
532
views
Is the meaning of "irreducible manifold", "not reducible to other manifold"?
This is a cross post of MSE.
Q1: What does "irreducible manifold" mean (not definition)?
My understanding of "irreducible manifold" is "is not reducible (homotopic or deformation or homeomorph or be …
- 4,195
2
votes
Is the meaning of "irreducible manifold", "not reducible to other manifold"?
Summary of comments and other sources
There are at least 4 similar concepts:
Irreducible smooth manifold: As Ryan Budney said, "Regarding high dimensions, generally irreducible manifolds do not exist …
- 4,195