The primary goal is to characterize Locally H-closed spaces (LHC), by conditions on the remainders of their extensions. These are also characterized using subspaces and extensions as well. Characterizing these classes in provide characterizations them terms boundaries. Recently, authors have proved that results give necessary sufficient for space be compact A number equivalences Hausdorff (Urys...

We introduce semicontinuity concepts for functions f with values in the space C(Y ) of closed convex subsets of a finite dimensional normed vector space Y by appropriate notions of upper and lower limits. We characterize the upper semicontinuity of f : X → C(Y ) by the upper semicontinuity of the scalarizations σf( · )(y∗) : X → R by the support function. Furthermore, we compare our semicontinu...

Let X be a metric space with metric p, let f(X)QX be a continuous mapping, and let h(X) ^X be a homeomorphism. For x&X, the s e t 23^-°o/(^) i called the semi-orbit of # under ƒ and the set n£XZh{x) is called the orbit of # under h. For # £ X , the closure of the semi-orbit of x under ƒ is called the semi-orbit-closure of x under ƒ and the closure of the orbit of x under h is called the orbit-c...

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...

Consider a gas of noninteracting particles diffusing into a semi-infinite lattice, Z+×ZD−1, subject to exclusion of double occupancy. An exact closed set of equations can be obtained and solved (in closed form) for the single-site occupancies or densities. Equations for the n-site occupancies couple only to such functions for n and n-1 sites, as for an infinite lattice. Their analysis reveals t...

The following is concerned with the in-the-large behavior of characteristics of differential equations on closed orientable manifolds. C+ will denote a positive semi-characteristic, C the set of co-limit2 points of C+, V the vector field defining the differential equation, M the manifold under consideration, and W the vector field orthogonal to V. In all that follows we shall assume that M is t...

Ever since the introduction of fuzzy sets by L. A. Zadeh [14], the fuzzy concept has invaded almost all branches of Mathematics. The concept of fuzzy topological space was introduced and developed by C.L. Chang [3] and since then many fuzzy topologists [1,6-13] have extended various notions in classical topology to fuzzy topological spaces. The concept of somewhat continuous functions was intro...

Today’s housing, as a private realm of human life, has changed in comparison with the past which was made regardless of quality, desirability, and lack of paying attention to the human needs and its psychological consequences; That is to say, residential units have turned into a set of closed spaces and their open and semi-open spaces have been merged into the urban spaces which disrupted their...

Consider a semi-algebraic set A in R constructed from the sets which are determined by inequalities pi(x) > 0, pi(x) ≥ 0, or pi(x) = 0 for a given list of polynomials p1, . . . , pm. We prove several statements that fit into the following template. Assume that in a neighborhood of a boundary point the semi-algebraic set A can be described by an irreducible polynomial f . Then f is a factor of a...