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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 18th 2017
• (edited May 18th 2017)

I am working on the entry topological manifold.

I gave it a subsection locally Euclidean spaces, which maybe eventually wants to be split off as an entry in its own right.

Now I have added statement and proof that locally Euclidean spaces are $T_1$, sober and locally compact (in the compact neighbourhood base sense): here.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 19th 2017

I have added statement and proof that locally Euclidean Hausdorff spaces are sigma-compact precisely if they are paracompact with a countable set of connected components: here

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 24th 2017

I have expanded the statement and proof of the local properties of locally Euclidean spaces (this prop.) to contain 1) $T_1$ 2) sobriety 3) local connectivity, 4) local compactness.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMay 24th 2017

Finally completed statement and proof of the equivalence of the three regularity conditions on locally Euclidean Hausdorff spaces here (the converse direction for second-countable had previously been missing)

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMay 24th 2017
• (edited May 24th 2017)

added statement and proof that open subspace of topological/differentiable manifolds are themselves such (here)

Used this to complete at general linear group the description as a Lie group (here)