A comparison of covering properties in T[lowered 3] and T[lowered 4] spaces

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1968

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Abstract

Weak and strong cover compactness are defined and compared with five other well-known covering properties in developable, semimetric, first countable, locally compact and general T[lowered 3] and T[lowered 4] spaces. In addition, it is shown that weak or strong cover compactness implies point-collectionwise normality in certain T[lowered 3] spaces and that this implication leads to useful results concerning subspaces, Cartesian product spaces and closed refinements. Finally, "basic" and "total" covering properties are defined, compared, and shown to insure the equivalence of large and small inductive dimension in metric spaces.

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