Martin Maria Kov\'ar
Which topological spaces have a weak reflection in compact spaces?

Comment.Math.Univ.Carolinae 36,3 (1995) 529-536.

Abstract:The problem, whether every topological space has a weak compact reflection, was answered by M. Hu\v{s}ek in the negative. Assuming normality, M. Hu\v{s}ek fully characterized the spaces having a weak reflection in compact spaces as the spaces with the finite Wallman remainder. In this paper we prove that the assumption of normality may be omitted. On the other hand, we show that some covering properties kill the weak reflectivity of a noncompact topological space in compact spaces.

Keywords: weak reflection, Wallman compactification, filter (base), net, $\theta $-regularity, weak $\left [\omega _1,\infty \right )^r$-refinability
AMS Subject Classification: Primary 54D35, 54C20; Secondary 54D20

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