Homeomorphism Groups and Metrisation of Manifolds

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New Zealand Journal of Mathematics

Vol. 42, (2012), Pages 37-43


David Gauld

Department of Mathematics

University of Auckland,

Auckland,

New Zealand

mailto:d.gauld@auckland.ac.nz

Jan van Mill

Faculty of Sciences

Department of Mathematics

VU University Amsterdam

1081 HV Amsterdam

The Netherlands

mailto:j.van.mill@vu.nl




Abstract We prove that a manifold M is metrisable if and only if its group of homeomorphisms \mathcal{H}(M) endowed with the compact-open topology is a q-space. We also discuss pseudo-character and tightness.

Keywords homeomorphism group, manifold, metrisation.

Classification (MSC2000) 54C35, 54E35.

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