Vol. 37, No. 2, 1971

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Semi-developable spaces and quotient images of metric spaces

Charles Compton Alexander

Vol. 37 (1971), No. 2, 277–293

In this paper semi-developable spaces are defined and, among T0-spaces, are shown to be the same as the semimetrizable spaces. Strongly semi-developable spaces are defined in a natural way and proven to coincide with an important class of semi-mefric spaces, namely those in which “Cauchy sequences suffice”. These spaces are shown to possess several other interesting properties. Probably the most significant of these is that the strongly semi-developable spaces are hereditarily quotient P-images of metric spaces. Other quotient images of metric spaces are similarly characterized in terms of semi-developments.

Mathematical Subject Classification 2000
Primary: 54D20
Received: 30 June 1989
Revised: 21 September 1970
Published: 1 May 1971
Charles Compton Alexander