Separation axioms and subcategories of top

On bD-Sets and Associated Separation Axioms

On Hereditary Coreflective Subcategories of Top

Let A be a topological space which is not finitely generated and CH(A) denote the coreflective hull of A in Top. We construct a generator of the coreflective subcategory SCH(A) consisting of all subspaces of spaces from CH(A) which is a prime space and has the same cardinality as A. We also show that if A and B are coreflective subcategories of Top such that the hereditary coreflective kernel o...

Splittability and Low Separation Axioms

The power and usefulness of cleavability (also known as splittability) have been well established within the framework of topology by A.V. Arhangel’skii and his associates. The concept was transferred to partially ordered sets by D.J. Marron and T.B.M. McMaster. The connections between topology and order are here exploited as we examine the properties enjoyed by a topological space that is spli...

Semi Separation Axioms and Hyperspaces

In this paper examples are given to show that s-regular and s-normal are independent; that s-normal, and s-regular are not semi topological properties; and that (S(X),E(X)) need not be I even if (X,T) is compact, s-normal, s-regular, semi-T2, and T0. Also, it is shown that for each space (X,T), (S(X) ,E(X)), (S(XO) ,E(Xo)), and (S(Xs0) ,E(Xs0)) are homeomorphic, where (X0, Q(X0)) is the T0-iden...

On rg - Separation Axioms

In this paper we define almost rg-normality and mild rg-normality, continue the study of further properties of rgnormality. We show that these three axioms are regular open hereditary. Also define the class of almost rg-irresolute mappings and show that rg-normality is invariant under almost rg-irresolute M-rg-open continuous surjection. AMS Subject Classification: 54D15, 54D10.