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On the Problem of Weak Reflections in Compact Spaces

In this paper we present, among others, an improvement of Hušek's characterization of the spaces with the weak compact reflection. Our main results are as follows: A topological space has a weak reflection in compact spaces iff the Wallman remainder is finite. If a θ‐regular or T1 space has a weak compact reflection, then the space is countably compact. A noncompact θ‐regular or T1 space which is weakly [ω1, ∞)r‐refinable, has no weak reflection in compact spaces.