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

6 votes
Accepted

A question about group action on topological space

Let's assume that $X$ is locally compact and instead of assuming that $G$ is a discrete group, assume more generally that it is locally compact and the action of $G$ on $X$ is continuous (i.e., the ma …
Dick Palais's user avatar
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10 votes
Accepted

local structure of free $\mathbb{R}$ actions

Such a theorem is proved for completely regular spaces $X$ in my article: On the Existence of Slices for Actions of Non-Compact Lie Groups, Richard S. Palais, The Annals of Mathematics, Second Series …
Dick Palais's user avatar
  • 15.3k
21 votes

Atiyah-Singer index theorem

I know it may seem rather "old", but the notes from the IAS "Seminar on the Atiyah-Singer Index Theorem from back in 1965 (published by Princeton Univ. Press) may be just what you are looking for, sin …
Dick Palais's user avatar
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4 votes

Compactness and Covering Spaces

Well, the obvious argument that any sequence has a convergent subsequence that your three friends used for the metrizeable case generalizes easily to show that any net has a convergent subnet in the g …
Dick Palais's user avatar
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14 votes

Why the triangle inequality?

From a conceptual standpoint, the triangle inequality per se is NOT what you really need. What I always emphasize when I teach metric spaces is that what gets used over and over again is that "two thi …
9 votes

When do isometric actions exist?

I am sorry That I am getting involved so late. I was away at a meeting for two days. I have an old (1961) paper in the ANNALS OF MATH called "On the Existence of Slices for Actions of Non-Compact Lie …
Dick Palais's user avatar
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