Some versions of relative paracompactness and their absolute embeddings. (English) Zbl 1199.54144

Kawaguchi, Shinji

Commentat. Math. Univ. Carol. 48, No. 1, 147-166 (2007).

Summary: We consider some versions of relative paracompactness defined by locally finite (not necessarily open) partial refinements or locally finite closed partial refinements, and also consider closure-preserving cases, such as \(1\)-\(l\!f\)-, \(1\)-\(cp\)-, \(\alpha \)-\(l\!f\)-, \(\alpha \)-\(cp\)-paracompactness and so on.

MSC:

54D20	Noncompact covering properties (paracompact, Lindelöf, etc.)
54D30	Compactness
54C20	Extension of maps
54C25	Embedding
54D10	Lower separation axioms (\(T_0\)–\(T_3\), etc.)

Keywords:

\(1\)-paracompactness of \(Y\) in \(X\); \(2\)-paracompactness of \(Y\) in \(X\); \(\alpha \)-paracompactness of \(Y\) in \(X\)