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Is a free and discrete group action on the plane a covering space action? Which polygons can be turned inside out by a smooth deformation? Jeff Strom 7, 2 2 gold badges 31 31 silver badges 62 62 bronze badges. BigbearZzz 2 2 silver badges 11 11 bronze badges. I'm looking If all length metrics are strong equivalent on a closed connected topology manifold?

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## Math 501: General Topology I

Structure of extensions arising in Lie approximation of connected groups My imperfect understanding is that, by the work of various authors Gleason, Yamabe, Montgomery, Zippin Yemon Choi Cardinal Invariants and Physics There are many applications of topology to physics, but I wonder if there is a known application of cardinal invariants to physics.

Gerardo Arizmendi 5 5 silver badges 13 13 bronze badges. Must a locally compact, second countable, Hausdorff space support a Radon measure? The motivation for this question comes from Anton Deitmar's paper On Alessandro Codenotti 2 2 silver badges 8 8 bronze badges. I previously asked In which topological spaces does the existence of a loop not contractable to a point imply there is a non-contractable simple loop also?

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Given the broad scope of this question I In which topological spaces does the existence of a loop not contractible to a point imply there is a non-contractible simple loop also? In another MathOverflow post I asked: In a topological space if there exists a loop that cannot be contracted to a point does there exist a simple loop that cannot be contracted also? Note that Is every closed subset of finite measure contained in an open subset of finite measure?

Michael 28 4 4 bronze badges. In a topological space if there exists a loop that cannot be contracted to a point does there exist a simple loop that cannot be contracted also?

## Questions tagged [general-topology]

I'm interested in whether one only needs to consider simple loops when proving results about simply connected spaces. If it is true that: In a Topological Space, if there exists a loop that cannot John McVey 1 1 silver badge 13 13 bronze badges. Sebastian K.

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Topological Structures. Historical Note. Exercises for 1. Exercises for 2. Exercises for 3.

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## General Topology | SpringerLink

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