A short note on fuzzy neighbourhood spaces

Morsi, Nehad N.

doi:10.1016/0165-0114(87)90052-2

Cited by 40 publications

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“…If (FCN) is fulfilled then N -( x ) = v~v A A c : X :~( Z )~s U p v (~) 2. Let Y fulfil the condition stipulated, let 8 E I ' and let 8 E lo.Choose n E No such that -58 and putting 12 define the fuzzy set which fulfila 1 8 + 8.…”

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On the Reflectiveness and Coreflectiveness of Subcategories of FTS

Löwen

Wuyts

Lowen

1989

Mathematische Nachrichten

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PreliminariesWe assume familiarity with most of the usual notational conventions in the field and limit ourselves to recalling only the most important concepts and definitions required in this paper.Our basic category is FTS which stands for the topological category [l] of fuzzy topological spaces and continous maps as introduced in [3]. MAX stands for the full isomorphism closed subcategory of l?TS which was essentially introduced in [9]. In order to reformulate its definition we recall the notion of level topologies introduced in [5]. J i (X, A ) E lFTSl and a E I, then the a-level topology of A is defined as r.(d) := {p-I(]a, 11) I p E A } . Then by definition (X, A ) E (MAX( if and only if for any other fuzzy topology r on X with level topologies identical to thosa of d, i.e. such that &.(A) = c,(P) for all a E I,, it follows that I'c d.If no confusion can occur, the topological space (X, &.(A)) is often shortly denoted FNS stands for the full isomorphism closed subcategory of FTS coneisting of those fuzzy topological spaces which are generated by a fuzzy neighborhood system. This category waa introduced in [6], and the objects are also called fuzzy neighborhood spaces. We recall that a fuzzy neighborhood system on a set X consists of a collection of prefilters ( J~( z ) ) , , ,~where -denotes the so-called saturation operation defined by b:= (4 I v E E I,, 3 4, E S:(#l, -E 5 4}.The family ( Y , ) , ,~ in (FN3) is called an €-kernel for Y.

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