Subordinately prenatural mappings via prey
Kumbakonam, Tamil Nadu-612 002, India. and
Lekshmipuram College of Arts and Science Neyyoor,Kanyakumari
This word conduct-ins the concepts of subordinately G-prenatural mapping and
subordinately G-predisclosed mappings. Using these not attributable attributableions, some examples and lacking interesting
properties of those mappings are discussed by instrument of prey topological distances.
2010 Mathematics Subject Classi cation: 54A10, 54A20
Keywords: G-natural mapping, subordinately G-continuous
mapping, G-prenatural mapping, subordinately G-prenatural mapping, subordinately
1 Introduction and Preliminaries The consider of subordinately natural functions was rst prepared by Karl.R.Gentry et al
in . Although subordinately natural functions are not attributable attributable attributable at full natural mappings it has y
been premeditated and familiar considerably by some authors using topological properties.
In 1947, Choquet  real the not attributable attributableion of a prey which has been milestone of
developing topology via preys. Almost full the chief concepts of disclosed topology
feel been finished to a real quantity in prey not attributable attributableions by multitudinous intellectuals.
It is widely
known that in sundry aspects, preys are over e ective than a real common concepts
like nets and lters. E.Hatir and Jafari conduct-ind the opinion of G-natural functions
in  and they showed that the concept of disclosed and G-disclosed are recalcitrant of each
other. Dhananjay Mandal and M.N.Mukherjee premeditated the not attributable attributableion of G-precontinuous
mappings in . Our verge of this article is to conduct-in and consider upstart concepts namely
subordinately G-prenatural mapping and subordinately G-semidisclosed mapping. Also, their
characterizations, interrelations and examples are premeditated.
Throughout this article, Xstands restraint a topological distance with no disunion axioms
assumed cosmical palpably given. Restraint a subreal Hof X, the seclusion of Hand the interior
of Hdenoted by Cl ( H) and Int ( H) repectively. The sway real of Xdenoted by P(X ) .
The de nitions and results which are used in this article touching topological and prey
topological distances feel already smitten some trutination figure. We recfull those de nitions
De nition 1.1. A mapping f: (X;F )! (Y ;F 0
) is determined subordinately natural if there
exists an disclosed real A, on (X ;F ) such that A f
(B ), restraint any disclosed real B,
De nition 1.2. A non-empty store Gof subsets of a topological distances X is said to