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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