1,720,975 research outputs found
On the fuzzes which are complete rings of sets
No full textObjects in the category of fuzzes whose underlying set is a complete ring of sets are described as subdirect products of particular elementar objects
alpha-star-compactness of the fuzzy unit interval
No full textAnswering a question raised by Gantner, Steinlage and Warren, we provide some conditions for the alpha-star-compactness of the fuzzy unit interval
-additive topological spaces
No full textWe investigate omega_mu-additive topological spaces, introduced by B. Sikorski, and related topics such as omega_mu-product topology, omega_mu-compactness, omega_mu-uniformity, and obtain some significant improvements of existing results
Some Results on omega_mu-metric spaces
No full textSome concepts used in valued spaces (spherical completeness and closure, pseudo-convergence) are introduced in the study of omega_mu-metric spaces; in this context such notions are discussed and employed to show some extensions of theorems well-known in metric spaces (contraction lemma, Baire's theorem, embedding of the generalized Cantor space)
Fuzzy proximities compatible with Lowen Fuzzy uniformities
No full textWe introduce a notion of fuzzy proximity which behaves well with respect to the fuzzy uniformities introduced by R. Lowen and prove some related results. We also provide some critical remarks about fuzzy topologies, fuzzy proximities and fuzzy uniformities
Some omega_mu-metrization theorems
No full textWe give a necessary and sufficient condition for a topological space to be omega_mu-metrizable (i.e. it admits a uniformity with a linearly ordered base of ccofinality omega_mu). This characterization, which extends a classic result of R.H. Bing, leads us to prove that the omega_mu-additive spaces which are either linearly ordered or omega_mu-compact are omega_mu-metrizable iff their diagonal is the intersection of a family of omega_mu-many open sets
On fuzzy metrizability
No full textWe answer two questions raised by M. A. Erceg [J. Math. Anal. Appl. 69 (1979), 205-230]: precisely we show that the fuzzy unit interval is never T0, except in the standard case, and that a fuzzy pseudo-metrizable T0 space is metrizable in the sense of Erceg (ibid.). Hence the two definitions of metrizable space given in B. Hutton and I. Reilly [Fuzzy Sets and Systems 3 (1980), 93-104] and Erceg (ibid.) are equivalent
Fuzzy uniformities induced by fuzzy proximities
No full textGiven a fuzzy proximity δ, we construct a fuzzy uniformity (in the sense of Lowen) which turns out to be the coarse stone among those which induce δ. We show that some basic theorems of general topology about precompact uniformities have a nice extension to fuzzy set topology
On the structure of fuzzes
No full textThe aim of this paper is to investigate the structure of fuzzes, introduced by Hutton. We shall not be concerned here with fuzzy topology, but we think that a deeper knowledge of the properties of fuzzes may be helpful in several fields of fuzzy set theory, and in the study of fuzzy topological spaces in particular
Uniform properties of normal and compact fuzzy topological spaces
No full textWe study some questions related to fuzzy uniformities, in the context introduced by Hutton. In particular, we prove the generalization of the following classical theorems.
1. Acompletely regular space is normal if and only if the family of finite open covers is a basis for a compatible uniformity.
2. A completely regular compact space admits exactly one compatible uniformity
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