We show that if L is a topological vector lattice, u:L→L the function u(x)=x∨0, C⊂L convex, and D=u(C) metrizable, then D an ANR u|C:C→D homotopy equivalence, so contractible thus AR. This proved by verifying hypotheses of second result: X connected space equivalent to ANR, Y f:X→Y continuous surjection such that, for each y∈Y neighborhood V⊂Y y, there V′⊂V y f−1(V′) can be contracted in f−1(V)...

The paper is an attempt to represent a study of limit points, boundary points, exterior points, border, interior points and closure points in the common generalized topological space. This paper takes a look at the possibilities of an extended topological space and it also considers the new characterizations of dense set.

Let L be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality and a temporal modality , understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language L by interpreting L in dynamic topological systems, i.e. ordered pairs 〈X, f 〉, where X is a topological space and f is a continuous function on X. Artemov...

Users of geographic databases that integrate spatial data represented in vector and raster models, should not perceive the differences among the data models in which data are represented, nor should they be forced to apply different concepts depending on the model in which spatial data are represented. A crucial aspect of spatial query languages for such integrated systems is the need mechanism...

Let Xo and X, be two Banach spaces which are continuously embedded in a common Hausdort t topological vector space. An admissible operator for the pair (Xo, X,) is a linear operator whose domain contains the union of the two spaces and whose restrictions to Xi is a bounded operator on Xi ( i = 0 , 1). A space X is called an interpolation space for the pair (Xo, X,) if each admissible operator T...

In this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. We also investigate effect to fuzzy soft connectedness. Moreover, $C_i$-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.

The Lie algebra of a nuclear group is a locally convex nuclear vector space. Mathematics Subject Classification (2000): 22B05, 22E65, 46Axx 1. The Lie Algebra of Abelian Topological Groups Let G be an abelian topological group. The set of all one–parameter–subgroups L(G) := {λ : R→ G : λ is a continuous homomorphism} is called the Lie algebra of G . We define addition pointwise and scalar multi...

It has been recently pointed out that black holes of constant curvature with a “chronological singularity” can be constructed in any spacetime dimension. These black holes share many common properties with the 2+1 black hole. In this contribution we give a brief summary of these new black holes and consider them as solutions of a Chern-Simons gravity theory. We also provide a brief introduction...

The main purpose of this paper consists of providing characterizations of the inclusion of the solution set of a given conic system posed in a real locally convex topological space into a variety of subsets of the same space de…ned by means of vector-valued functions. These Farkas-type results are used to derive characterizations of the weak solutions of vector optimization problems (including ...