For a non-degenerate convex subset Y of the n-dimensional Euclidean space Rn , let K(Y ) be the family of all fuzzy sets of Rn , which are upper-semicontinuous, fuzzy convex and normal with compact supports contained in Y. We show that the space K(Y ) with the topology of endograph metric is homeomorphic to the Hilbert cube Q = [−1, 1] iff Y is compact; and the space K(Y ) is homeomorphic to {(...

in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.

A topological space X is said to be semi-re-connected at a point xGA" provided there exists an open set U containing x such that every Cech re-cycle on a compact subset of U bounds on X. (If X is regular, "a compact subset of" may be omitted.) If X is semi-re-connected at every point, then X is said to be semi-w-connected [l].2 As shown in [l], if a space has a finite 1-dimensional Betti number...

according to statistics, in 2009 iran’s oil and gas consumption were 1.4 and 3.1 times higher than the world average and during 1998 to 2008 residential sector accounted for 42% of the total energy consumption in the country. as hot-humid climate is the most severe climate across the world, climatic consideration must be incorporated in design of the new dwellings in this area. over the centuri...

The concept of fuzzy set was introduced by Zadeh in his classical paper [1]. This concept provides a natural foundation for treating mathematically the fuzzy phenomena, which exist pervasively in our real world, and for building new branches of fuzzy mathematics. In the area of Fuzzy Topology, introduced by Chang [2], much attention has been paid to generalize the basic concepts of General Topo...

In this paper we introduce and study the neutrosophic crisp pre-open, semi-open, βopen set, neutrosophic crisp continuity and neutrosophic crisp compact spaces are introduced. Furthermore, we investigate some of their properties and characterizations. Possible application to GIS topology rules are touched upon.