Two Classes of Infrasoft Separation Axioms

On bD-Sets and Associated Separation Axioms

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.

Fuzzy Minimal Separation Axioms

In this paper, we deal with some separation axioms in the context of fuzzy minimal structures.

Complexity Classes as Mathematical Axioms

Complexity theory, being the metrical version of decision theory, has long been suspected of harboring undecidable statements among its most prominent conjectures. Taking this possibility seriously, we add one such conjecture, P 6= NP , as a new “axiom” and find that it has an implication in 3-dimensional topology. This is reminiscent of Harvey Friedman’s work on finitistic interpretations of l...

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...