Vol. 61, No. 1, 1975

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Local connectedness in developable spaces

Harold W. Martin

Vol. 61 (1975), No. 1, 219–224

A space is spherically connected if and only if it has an admissible semi-metric d such that d-spheres of radius less than one are connected. It is shown that a developable space is locally connected if and only if it is spherically connected. A semi-metric space is K-semi-metrizable if and only if it admits a semi-metric d such that d(A,B) > 0 whenever A and B are disjoint compact sets. It is shown that in the class of locally connected rim compact spaces, the K-semi-metrizable spaces are precisely the developable γ-spaces. An example is given of a locally connected, locally compact K-semi-metrizable Moore space which is not metrizable.

Mathematical Subject Classification 2000
Primary: 54E25
Secondary: 54E35
Received: 12 March 1975
Revised: 17 August 1975
Published: 1 November 1975
Harold W. Martin