The probability measures on compact Hausdorff spaces K form a compact convex subset PK of the space of measures with the vague topology. Every continuous map f : K → L of compact Hausdorff spaces induces a continuous affine map Pf : PK → PL extending P. Together with the canonical embedding ε : K → PK associating to every point its Dirac measure and the barycentric map β associating to every pr...

in this paper, some fundamental concepts are given relating to fuzzytopological spaces. then it is shown that there is a contravariant functorfrom the category of the pointed fuzzy topological spaces to the category ofgroups and homomorphisms. also the fuzzy topological spaces which are hopfspaces are investigated and it is shown that a pointed fuzzy toplogicalspace having the same homotopy typ...

Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:Krightarrow E$ is a continuous mapping, then there exi...

In functional analysis it is well known that every linear functional defined on the dual of a locally convex vector space which is continuous for the weak topology is the evaluation at a uniquely determined point of the given vector space. M. Schröder and A. Simpson have obtained a similar result for lower semicontinuous linear functionals on the cone of all Scott-continuous valuations on a top...

Given a natural correspondence between a family of inequalities and a closed convex set in a topological linear space, one might expect that an inequality corresponding to a special point (e.g., an extreme point) would be of special interest in view of the convex analysis theory. In this paper, we realize this concept. Let X be an arbitrary set and {φ0,φ1,φ} a triple of nonnegative real-valued ...

Categorifying the concept of topological group, one obtains the notion of a ‘topological 2-group’. This in turn allows a theory of ‘principal 2-bundles’ generalizing the usual theory of principal bundles. It is well-known that under mild conditions on a topological group G and a space M , principal G-bundles over M are classified by either the Čech cohomology Ȟ(M, G) or the set of homotopy clas...

We define and study a class of finite topological spaces, which model the cell structure of a space obtained by gluing finitely many Euclidean convex polyhedral cells along congruent faces. We call these finite topological spaces, combinatorial cell complexes (or c.c.c). We define orientability, homology and cohomology of c.c.c’s and develop enough algebraic topology in this setting to prove th...

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.

We give a lower bound on the number of periodic billiard trajectories inside a generic smooth strictly convex closed surface in 3-space: for odd n, there are at least 2(n − 1) such trajectories. Convex plane billiards were studied by G. Birkhoff, and the case of higher dimensional billiards is considered in our previous papers. We apply a topological approach based on the calculation of cohomol...