Abstract

On Soft Nano Resolvable and Soft Nano Irresolvable Spaces

P. G. Patil1* and Spoorti S. Benakanawari2

1,2Department of Mathematics, Karnatak University Dharwad-580003, Karnataka, INDIA. pgpatil01@gmail.com1 (Corresponding Author) and spoortisb@gmail.com2

DOI : http://dx.doi.org/10.29055/jcms/1003

ABSTRACT

A soft nano topological space is called soft nano resolvable space if it can be expressed as a union of two soft nano disjoint dense sets, otherwise it is termed as soft nano irresolvable. In this paper, soft nano resolvable and soft nano irresolvable spaces are introduced and relationship between soft nano dense, soft nano codense and soft nano nowhere dense set is established. New characterizations of soft nano irresolvable spaces in terms of soft nano almost open (preopen) sets are studied. Also, several weaker forms of soft nano irresolvable are introduced. Several new results of soft nano open hereditarily irresolvable spaces are obtained and precise relationships are noted between soft nano open hereditarily irresolvability, soft nano irresolvability and soft nano hereditarily irresolvability. A study on levels of soft nano irresolvability is examined. Also, a brief note on functions and soft nano irresolvability is discussed. Results pertaining to soft nano extremally disconnected spaces are obtained. 2010 AMS Subject classification: 54A05, 54A10.

Keywords :Soft nano resolvable spaces, soft nano irresolvable spaces, soft nano open hereditarily irresolvable spaces.

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