Metrisability of Manifolds in Terms of Function Spaces

David Gauld and Frederic Mynard


We present conditions on the space of continuous real-valued functions on a topological manifold, either with the compact-open or pointwise convergence topology, which are equivalent to metrisability of the manifold. In addition we display some covering and related properties which are also equivalent to metrisability for a manifold.

manifold, metrisability, function space, Polish, countable tightness

Math Review Classification
Primary 54E35, 54C35, 57N15 ; Secondary 46E10

Last Updated
4 July, 2001

13 pages

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