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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 1T_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 1T_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)