Weakly α

In this paper, we introduce the notion of weakly α-continuous functions in topological spaces. Weak α-continuity and subweak continuity due to Rose [1] are independent of each other and are implied by weak continuity due to Levine [2]. It is shown that weakly α-continuous surjections preserve connected spaces and that weakly α-continuous functions into regular spaces are continuous. Corollary 1 of [3] and Corollary 2 of [4] are improved as follows: If f1:X→Y is a semi continuous function into a Hausdorff space Y, f2:X→Y is either weakly α-continuous or subweakly continuous, and f1=f2 on a dense subset of X, then f1=f2 on X

Pseudo perfectly continuous functions and closedness/compactness of their function spaces

[EN] A new class of functions called 'pseudo perfectly continuous' functions is introduced. Their place in the hierarchy of variants of continuity which already exist in the literature is highlighted. The interplay between topological properties and pseudo perfect continuity is investigated. Function spaces of pseudo perfectly continuous functions are considered and sufficient conditions for their closedness and compactness in the topology of pointwise convergence are formulated.Kohli, J.; Singh, D.; Aggarwal, J.; Rana, M. (2013). Pseudo perfectly continuous functions and closedness/compactness of their function spaces. Applied General Topology. 14(1):115-134. doi:10.4995/agt.2013.1622.SWORD11513414

Remarks on locally closed set

See PD

Minimal structures, punctually m-open functions in the sense of Kuratowski and bitopological spaces

Byusingm-open functions from a topological space into an m-space, we establish the unified theory for several weak forms of open functions in the sense of Kuratowski between bitopological spaces