Abstract:
We investigate resolvability at a point of regular Lindelöf and pseudocompact spaces. We also generalize results of E.G. Pytkeev on resolvability and resolvability at a point of regular countably compact spaces. In particular, we prove the following statement. Suppose a space $X$ is regular and every infinite subset of $X$ with cardinality smaller than $\kappa>\omega$ has a complete accumulation point. Then $X$ is $\min\{\kappa, \Delta(X)\}$-resolvable.
Key words:resolvability, resolvability at a point, pseudocompactness, countable compactness, Lindelöf spaces, extent.
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