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Point-countable covers and k-networks. (English) Zbl 0676.54035
The author defines properties \(C_ 1\), \(C_ 2\), \(C_ 3\) for networks. These are weakenings of the notions of cs-network and k-network. After discussing the relationships among these properties and the k-network and cs-network properties, he uses these notions to give characterizations of certain quotient s-images of metric spaces and to give conditions for the developability of strict p-spaces and \(w\Delta\)-spaces.
Reviewer: S.W.Davis

MSC:
54E20 Stratifiable spaces, cosmic spaces, etc.
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54E18 \(p\)-spaces, \(M\)-spaces, \(\sigma\)-spaces, etc.
54E30 Moore spaces
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