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Results tagged with homotopy-theory
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user 17029
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
10
votes
Why the "W" in CGWH (compactly generated weakly Hausdorff spaces)?
Here is perhaps the simplest example of a CGWH space which fails to be Hausdorff.
Start with a countable metric space $X$ so that with one exception $x$, each point is open, but so that at the excepti …
- 1,968
11
votes
Are the higher homotopy groups of the Hawaiian earring trivial?
Here is a short natural argument that planar continua are aspherical, different from the technique of Cannon/Conner/Zastrow, and straight forwardly applied to the Hawaiian earring.
The Hawaiian earr …
- 1,968
3
votes
Homotopy problem for infinite dimensional topological space II
The following does not settle the original question.
The answer is `no' if we ignore the intrinsic metric requirement and merely demand metric.
For a counterexample first observe that the inverse li …
- 1,968