The theory of global fuzzy neighborhood structures Part I — The general case

On -proximities of the internal type

“…By a global L-neighborhood structure on a set X [8] we mean a mapping h : F L X → F L X such that the following conditions are fulfilled:…”

“…A mapping f : (X, h) → (Y, k) between global L-neighborhood spaces is said to be (h, k)-continuous [8] provided (2) In the general case of L, the mapping h :…”

“…for each M ∈ F L X, where N is the set of all positive integers [3,8]. Let (N i ) i∈I be a family of L-topogenous structures N i on sets X i and (f i ) i∈I a family of mappings f i of a set X into X i .…”

“…The symmetry of the global L-neighborhood structure [8] and of the L-uniform structure [10] is defined independently of an order-reversing involution of L. Hence, the L-proximity of the internal type has a good relation with these structures and then this proximity is more suitable to our study in this paper.…”

“…We may note that, in this paper, we use the term "L" instead of the term "fuzzy" (in case of fuzzy topogenous structures, fuzzy proximities of the internal type, global fuzzy neighborhood structures and fuzzy uniform structures) which is used in [8][9][10].…”