Notes on characterization of paracompact frames. (English) Zbl 0672.54018

Pultr, Aleš; Úlehla, Josef

Commentat. Math. Univ. Carol. 30, No. 2, 377-384 (1989).

Summary: A proof of several characteristics of paracompactness in the general localic setting using a procedure very similar to the classical one is presented. Among these, the characterizations concerning full normality and \(\sigma\)-local finiteness have been proved by other techniques before; we add characterizations by the existence of locally finite quasirefinements, and of \(\sigma\)-discrete refinements.

MSC:

54D20	Noncompact covering properties (paracompact, Lindelöf, etc.)
54F05	Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
06D99	Distributive lattices

Keywords:

paracompact frames; paracompactness; general localic setting; full normality; \(\sigma\)-local finiteness; existence of locally finite quasirefinements; \(\sigma\)-discrete refinements