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We show that every T 1 wN-space is expandable and as a corollary, we prove that a θ-renable sym-wg T 1 space is paracompact and thus two problems of Chris Good are solved. We also investigate s-expandability, and for extremally disconnected spaces, a characterization of s-expandability is given in terms of covers, which gives an extension to a known result.

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In this paper, β-compactness is introduced in L-topological spaces, where L is a fuzzy lattice. And its topological properties are systematically studied. This β-compactness is defined for arbitrary L-subsets. The intersection of a β-compact Lfuzzy subset and a β-closed L-fuzzy subset is β-compact with a good extension. Also different characterizations are obtained and some of its properties are studied.