On Lattice - Topological Properties of General Wallman Spaces Carmen Vlad
نویسنده
چکیده
Let X be an arbitrary set and a lattice of subsets ofX such that t/t, X E ..A() is the algebra generated by and I() consists of all zero-one valued finitely additive measures on Various subsets of I() are considered and certain lattices are investigated as well as the topology of closed sets generated by them. The lattices are investigated for normality, regularity, repleteness and completeness. The topologies are similarly discussed for various properties such as T2 and Lindel0f
منابع مشابه
Normal Characterizations of Lattices
Let X be an arbitrary nonempty set and a lattice of subsets of X such that ∅, X ∈ . Let ( ) denote the algebra generated by and I( ) denote those nontrivial, zero-one valued, finitely additive measures on ( ). In this paper, we discuss some of the normal characterizations of lattices in terms of the associated lattice regular measures, filters and outer measures. We consider the interplay betwe...
متن کاملTopological Aspects of the Product of Lattices
Let X be an arbitrary nonempty set and L a lattice of subsets of X such that ∅, X ∈ L. A L denotes the algebra generated by L, andM L denotes those nonnegative, finite, finitely additive measures on A L . In addition, I L denotes the subset of M L which consists of the nontrivial zeroone valued measures. The paper gives detailed analysis of products of lattices, their associated Wallman spaces,...
متن کامل-smoothness Criteria for Lattice Measures
Let X be an abstract set and L a lattice of subsets of X such that ;; X 2 L. In this paper we extend smoothness characterizations of L regular measures 2 MR(L) to the general case of 2 M (L), by considering different outer measures associated with and the induced measure on a Wallman space.
متن کاملON STRATIFIED LATTICE-VALUED CONVERGENCE SPACES
In this paper we provide a common framework for different stratified $LM$-convergence spaces introduced recently. To this end, we slightly alter the definition of a stratified $LMN$-convergence tower space. We briefly discuss the categorical properties and show that the category of these spaces is a Cartesian closed and extensional topological category. We also study the relationship of our cat...
متن کاملWeak hyper semi-quantales and weak hypervalued topological spaces
The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued t...
متن کامل