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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
17
votes
Accepted
Co-Hausdorffification
The procedure you describe does not produce a $T_2$-space in general. You can read here and here on MO, and also this nice recent bachelor thesis by Bart van Munster. But you do get the Hausdorffifica …
1
vote
0
answers
178
views
Topological characterisation of loop spaces
Let $\Omega\colon \mathrm{Top}_*\to\mathrm{Top}_*$ be the loop space functor assigning to each pointed topological space $X$ the pointed space consisting of all based continuous maps $S^1\to X$ equipp …
1
vote
1
answer
169
views
Non-compact structure group and compactly supported gauge transformations
Let $\pi\colon P\to X$ be a locally trivial principal $G$-bundle over a Hausdorff paracompact space $X$, where $G$ is a topological group (we work in the category of topological spaces, as I do not th …