Browsing by Author "R. Lowen"

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FTS0: The epireflective hull of the Sierpinski object in FTS
(1989) R. Lowen; Arun K. Srivastava
In the category TOP of topological spaces, the epireflective hull of the standard two-point Sierpinski space is known to coincide with the subcategory of T0 topological spaces. In this note, we determine the epireflective hulls of the recently found 'Sierpinski objects' in the categories FTS, FNS and ω(TOP) of, respectively, fuzzy topological spaces, fuzzy neighborhood spaces and topologically generated fuzzy topological spaces. We thereby identify the corresponding 'T0-objects' in these categories and note that the categories FTS, FNS and ω(TOP) are 'universal'. © 1989.
On Preuss' connectedness concept in FTS
(1992) R. Lowen; Arun K. Srivastava
the principal aim of this paper is to examine the extent to which certain connectedness concepts in FTS can be viewed as connectedness in Preuss' sense i.e., as subclasses of [FTS] which equal CE:= {X ε{lunate} ∥FTS∥ ∥ f{hook} ε{lunate} FTS(X, Y), Y ε{lunate} E ⇒ f{hook} is constant}, for some E ⊂ ∥FTS∥. Two new connectedness concepts in FTS, which subsume an existing concept, are shown capable of being so viewed while it turns out that certain existing, otherwise good, connectedness concepts cannot be so viewed. © 1992.
Sierpinski objects in subcategories of FTS
(1988) R. Lowen; A.K. Srivastava
E.G. Manes gave a characterization of the category of topological spaces as a suitable category of sets with structure having an appropriate “Sierpinski object”. By identifying an appropriate Sierpinski object, A.K. Srivastava and R. Srivastava obtained an analogous characterization of the category of fuzzy topological spaces. In the present paper, we extend these ideas further and give similar characterizations of the categories of fuzzy neighbourhood spaces and topological fuzzy topological spaces by identifying appropriate Sierpinski objects in these categories. AHS Subject Classifications : 54A40. 54B30, 18R30. 18B99, 18A40. © 1988 Taylor & Francis Group, LLC.