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A new approach to nearly compact spaces. (English) Zbl 1400.54036

Summary: Using the covers formed by pre-open sets, we introduce and study the notion of po-compactness in topological spaces. The notion of po-compactness is weaker than that of compactness but stronger than semi-compactness. It is observed that po-compact spaces are the same as nearly compact spaces. However, we find new characterizations to near compactness, when we study it in the sense of po-compactness.

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54A05 Topological spaces and generalizations (closure spaces, etc.)
54D30 Compactness
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