This paper is a continuation of [1]. That is, it considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying [2]. It investigates topological notions defined by means of a-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Łukasiewicz logic in [0,1]). Other characterizations of fuzzifying compactness are given, including characterizations in terms of nets and a-subbases. Several characterizations of locally a-compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.

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