Vol. 59, No. 1, 1975

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Finite-to-one open maps of generalized metric spaces

Raymond F. Gittings

Vol. 59 (1975), No. 1, 33–41

We investigate the invariance of certain classes of generalized metric spaces under finite-to-one open maps. In particular, the following classes of spaces are invariant: wΔspaces, β-spaces, Σ#-spaces, -spaces, γ-spaces, quasi-metriza. ble T1-spaces, a-spaces and Moore spaces. Several applications are given, including a metrization theorem via finite-to-one open maps. We also show that M-spaces, wM-spaces, wN-spaces, and Mi-spaces (i = 1,2,3) are not necessarily preserved by finite-to-one open maps. Further, an example is presented which shows that some of those classes of space which are invariant under finite-to-one open maps are not necessarily invariant under compact open maps.

Mathematical Subject Classification 2000
Primary: 54C10
Secondary: 54E35
Received: 3 April 1974
Published: 1 July 1975
Raymond F. Gittings