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There has been renewed interest in recent years in McKinsey and Tarski’s interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the modal mu-calculus and to a logic of tangled closure operators that was developed by Fernández-Duque after these two languages had been shown by Dawar and Ot...

Abstract In this paper we formulate a setvalued fixed point problem by combining four prevalent trends of theory. We solve the showing that set points is nonempty. Further have data dependence result pertaining to and also stability for sets. The main extended metric spaces with graph. results are obtained without use completeness assumption which replaced some other conditions suitable solving...

The aim of this study is to investigate the effects of timbre, the presence or absence of tonal hierarchy, and the influence of musical training on the perception of "tension-relaxation schemas" in musical phrases. Two musical excerpts taken from the Baroque 'tonal/metric' and contemporary 'nontonal/nonmetric' repertoires constituted the stimuli of the experiment. Two versions of each excerpt w...

in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

the present paper introduces the notion of the complete fuzzy norm on a linear space. and, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. some characterizations of their properties are obtained.

Generalising Nachbin's theory of ``topology and order'', in this paper we   continue the study of quantale-enriched categories equipped with a compact   Hausdorff topology. We compare these $V$-categorical compact Hausdorff spaces   with ultrafilter-quantale-enriched categories, and show that the presence of a   compact Hausdorff topology guarantees Cauchy completeness and (suitably   defined) ...

G. Birkhoff [l] and H. Samelson [4] have shown that a means of solving problems concerning the existence and uniqueness of eigenvectors of positive operators is given by introducing a suitable metric on a subset of the cone with respect to which the operators are contractions. More specifically, they have proved the Perron theorem for matrices with positive elements by intersecting the positive...

We propose a logic for reasoning about metric spaces with the induced topologies. It combines the ‘qualitative’ interior and closure operators with ‘quantitative’ operators ‘somewhere in the sphere of radius r,’ including or excluding the boundary. We supply the logic with both the intended metric space semantics and a natural relational semantics, and show that the latter (i) provides finite p...