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Edge of the World: When Are Manifolds Metrisable?

In: Non-metrisable Manifolds

Author

Listed:
  • David Gauld

    (University of Auckland, Department of Mathematics)

Abstract

This chapter might seem odd in that it lists a huge number of topological properties and connections between them. What it shows is that the requirement that a manifold be metrisable is extremely versatile. We list over 100 conditions each of which is equivalent to metrisability of a manifold. At one extreme, metrisability of a manifold implies that it may be embedded as a closed subset of some Euclidean space while at the other extreme knowing that every open cover of the form $$\{U_{\alpha }\ /\ {\alpha }

Suggested Citation

  • David Gauld, 2014. "Edge of the World: When Are Manifolds Metrisable?," Springer Books, in: Non-metrisable Manifolds, edition 127, chapter 0, pages 21-36, Springer.
    • Handle: RePEc:spr:sprchp:978-981-287-257-9_2
    DOI: 10.1007/978-981-287-257-9_2
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