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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

6 votes
1 answer
227 views

Example similar to the Griffiths twin cone but with fundamental group that allows surjection...

The Griffiths twin cone is an example of a wedge sum of two contractible spaces being non-contractible. Namely, it is the wedge sum $\mathbb G=C\mathbb H\vee_p C\mathbb H$ of two coni over the Hawaiia …
2 votes
0 answers
90 views

First Betti number of a Reeb graph is not greater than that of the space?

(I have asked this question at math stackexchange, it was upvoted but got no answers; maybe you can help.) It is well-known that $\beta_1(R(f))\le\beta_1(X)$, where $\beta_1$ is the first Betti numbe …