A duality theorem for the category of locally compact Hausdorff spaces and continuous maps which generalizes the well-known Duality Theorem of de Vries is proved. 2000 MSC: primary 18A40, 54D45; secondary 06E15, 54C10, 54E05, 06E10.

A duality theorem for the category of locally compact Hausdorff spaces and continuous maps which generalizes the well-known Duality Theorem of de Vries is proved. 2000 MSC: primary 18A40, 54D45; secondary 06E15, 54C10, 54E05, 06E10.

in this paper we develop a natural generalization of schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. we prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. we prove that the operators of a dual ov-basis are continuous. we also dene the concepts of bessel, hilbert ov-basis and obt...

We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We give the operator that is semi-compact, but it is not bweakly. W...

Powar P. L. and Rajak K., have introduced fine-topological space which is a special case of generalized topological sspace. In this paper, the author has introduced a new class of functions called fine weakly BR-continuous functions on fine topological space (cf. [12]). Weakly BR-continuous functions has been introduced by Ekici [3] which includes the class of strongly continuous functions due ...

A topology τ on a fixed nonempty set X is said to satisfy the weakly continuous representation property if every weakly continuous not necessarily total preorder on the topological space (X, τ) admits a continuous order preserving function. Such a property generalizes the well known continuous representation property of a topology τ on a set X (according to which every continuous total preorder...

The concept of unitary duality for topological groups was introduced by H. Chu. All mapping spaces are given the compact-open topology. Let G and H be locally compact groups. G" is the space of continuous finite-dimensional unitary representations of G. Let Horn (C, H") denote the space of all continuous maps from G" to H" which preserve degree, direct sum, tensor product and equivalence. We pr...

Reachability and observability criteria are obtained for 2D continuous-discrete time-variable Attasi type systems by using suitable 2D reachability and observability Gramians. Necessary and sufficient conditions of reachability and observability are derived for time-invariant systems. The duality between the two concepts is emphasized as well as their connection with the minimality of these sys...

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...