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Change of topology, characterizations and product theorems for semilocally $$P$$-spaces. (English) Zbl 0781.54007
If $$P$$ is a topological property, a set with this property is called a $$P$$-set. The author defines a “semilocally $$P$$-space” to be a topological space satisfying this condition: for each point $$x$$ and each open neighborhood $$U$$ of $$x$$, there is an open neighborhood $$V$$ of $$x$$ which is contained in $$U$$ and whose complement is the union of finitely many closed $$P$$-sets. The product theorem of the title gives conditions under which the product of such spaces is again such a space. This unifies and extends some known results for properties which include: connectedness, several forms of compactness, various versions of regularity and complete regularity.
Reviewer: P.R.Meyer (Bronx)

##### MSC:
 54B10 Product spaces in general topology 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)