Vol. 47, No. 2, 1973

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Mapping spaces and cs-networks

Joe Alston Guthrie

Vol. 47 (1973), No. 2, 465–471

In this paper the space of maps from an 0-space to a space Y is studied by means of convergent sequence-networks. The notion of a cs σ-space, a simultaneous generalization of metric spaces and 0-spaces, is defined, and it is shown that if Y is a (paracompact) csσ-space then the mapping space from X to Y is a (paracompact) csσ-space when equipped with either the compact-open or the cs-open topology. It is proved that the compact sets are the same in the two topologies. The class of cs σ-spaces and the class of -spaces introduced by 0 ‘Meara are shown to be identical in the presence of paracompactness.

Mathematical Subject Classification 2000
Primary: 54C35
Received: 18 February 1971
Revised: 15 November 1972
Published: 1 August 1973
Joe Alston Guthrie