The notion of fuzzy filters was studied by Vicente and Aranguren (1988), Lowen (1979), and Ramakrishnan and Nayagam (2002). The notion of fuzzily compactness was introduced and studied by Ramakrishnan and Nayagam (2002). In this paper, an equivalent condition of fuzzily compactness is studied and a new notion of semi-Hausdorffness on fuzzy filters, which cannot be defined in crisp theory of filters, is introduced and studied.
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