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Study of covering properties in fuzzy topology
This work is devoted to the study of covering properties both in L-fuzzy topological spaces and in smooth L-fuzzy topological spaces , that is the fuzzy spaces in Sostak's sense, where L is a fuzzy lattice . Based on the satisfactory theory of L-fuzzy compactness build up by Warner, McLean and Kudri, good definitions of feeble compactness and P-closedness are introduced and studied. A unification theory for good L-fuzzy covering axioms is provided.
Following the lines of L-fuzzy compactness, we suggest two kinds of L-fuzzy relative compactness as in general topology, study some of their properties and prove that these notions are good extensions of the corresponding ordinary versions.
We also present L-fuzzy versions of R-compactness , weak compactness and 0-rigidity and discuss some of their properties.
By introducing 'a-Scott continuous functions', a 'goodness of extension' criterion for smooth fuzzy topological properties is established. We propose a good definition of compactness, which we call 'smooth compactness' in smooth L-fuzzy topological spaces. Smooth compactness turns out to be an extension of L-fuzzy compactness to smooth L-fuzzy topological spaces. We study some properties of smooth compactness and obtain different characterizations. As an extension of the fuzzy Hausdorffness defined by Warner and McLean, 'smooth Hausdorffness' is introduced in smooth L-fuzzy topological spaces. Good definitions of smooth countable compactness, smooth Lindelofness and smooth local compactness are introduced and some of their properties studied
Edgeworth and Walras equilibria of an arbitrage-free exchange economy
In this paper, we first give a direct proof of the existence of Edgeworth equilibria for exchange economies with consumption sets which are (possibly) unbounded below. The key assumption is that the individually rational utility set is compact. It is worth noticing that the statement of this result and its proof do not depend on the dimension or the particular structure of the commodity space. In a second part of the paper, we give conditions under which Edgeworth allocations can be decentralized by continuous prices in a finite dimensional and in an infinite dimensional setting. We then show how these results apply to some finance models.Arbitrage-free asset markets; individually rational utility set; Edgeworth equilibria; fuzzy coalitions; fuzzy core; Walras equilibria; quasiequilibria; properness of preferences
String Theory and the Fuzzy Torus
We outline a brief description of non commutative geometry and present some
applications in string theory. We use the fuzzy torus as our guiding example.Comment: Invited review for IJMPA rev1: an imprecision corrected and a
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(R1960) Connectedness and Compactness in Fuzzy Nano Topological Spaces via Fuzzy Nano Z Open Sets
In this paper, we study the notion of fuzzy nano Z connected spaces, fuzzy nano Z disconnected spaces, fuzzy nano Z compact spaces and fuzzy nano Z separated sets in fuzzy nano topological spaces. We also give some properties and theorems of such concepts with connectedness and compactness in fuzzy nano topological spaces
On fuzzy weakly-closed sets
A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy
topological space is introduced and it is established that this class of fuzzy
closed sets lies between fuzzy closed sets and fuzzy generalized closed sets.
Alongwith the study of fundamental results of such closed sets, we define and
characterize fuzzy weakly compact space and fuzzy weakly closed space
How regular can maxitive measures be?
We examine domain-valued maxitive measures defined on the Borel subsets of a
topological space. Several characterizations of regularity of maxitive measures
are proved, depending on the structure of the topological space. Since every
regular maxitive measure is completely maxitive, this yields sufficient
conditions for the existence of a cardinal density. We also show that every
outer-continuous maxitive measure can be decomposed as the supremum of a
regular maxitive measure and a maxitive measure that vanishes on compact
subsets under appropriate conditions.Comment: 24 page
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