Somewhat precontinuous mappings via grill Essay

Subordinately prenatural mappings via prey

A. Swaminathany

Department of Mathematics

Government Arts College(Autonomous)

Kumbakonam, Tamil Nadu-612 002, India. and

M. Sankari

Department of Mathematics

Lekshmipuram College of Arts and Science Neyyoor,Kanyakumari

Tamil Nadu-629 802, India.

Abstract

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

G -predisclosed mapping. G-predense real.

1 Introduction and Preliminaries The consider of subordinately natural functions was rst prepared by Karl.R.Gentry et al

in [4]. Although subordinately natural functions are not attributable attributable attributable at full natural mappings it has y

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1

2

been premeditated and familiar considerably by some authors using topological properties.

In 1947, Choquet [1] 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 [3] 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 [2]. 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

and basic properties as follows:

De nition 1.1. A mapping f: (X;F )! (Y ;F 0

) is determined subordinately natural[4] if there

exists an disclosed real A, on (X ;F ) such that A f

1

(B ), restraint any disclosed real B,

on (Y ;F 0

) .

De nition 1.2. A non-empty store Gof subsets of a topological distances X is said to

be a prey[1] on X if (i)

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