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Results tagged with gn.general-topology
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user 1198
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
15
votes
Finite Hausdorff spaces
Yes. Better, it works for $T_1$, too: $T_1$ is the axiom that one-point sets are closed.
Then since the set is finite, the complement of any point is also closed; the point is open. That's the discr …
- 2,018
2
votes
Freeing a sphere from within a sphere
Edit: This is meant to answer the question of why we can't have an embedding $\mathbb S^{n-1}\times I\hookrightarrow\mathbb R^n$ such that the boundary is two side-by-side spheres rather than two nest …
- 2,018
1
vote
What are the topological properties of the metric space retained (inherited) for its completion
I was going to suggest that all the connectivity properties were either preserved or sometimes acquired by completion: e.g. a totally disconnected $X$ may become a path-connected $\bar X$, and the sam …
17
votes
understanding Steenrod squares
I second the references to Hatcher and to Mosher & Tangora, though you can also find Steenrod's original paper. At least the first two of those start out by listing the various axioms of Steenrod squ …
- 2,018