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weak reflection; Wallman compactification; filter (base); net; $\theta$-regul\-arity, weak $\left[\omega_1, \infty\right)^r$-refinability
The problem, whether every topological space has a weak compact reflection, was answered by M. Hu\v sek in the negative. Assuming normality, M. Hu\v sek 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.
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