Somewhat precontinuous mappings via grill Essay

Slightly preregular mappings via martyr

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.


This expression prefaces the concepts of slightly G-preregular mapping and

slightly G-prepublic mappings. Using these referableions, some examples and scant interesting

properties of those mappings are discussed by media of martyr topological boundlessnesss.

2010 Mathematics Subject Classi cation: 54A10, 54A20

Keywords: G-regular mapping, slightly G-continuous

mapping, G-preregular mapping, slightly G-preregular mapping, slightly

G -prepublic mapping. G-predense regular.

1 Introduction and Preliminaries The consider of slightly regular functions was rst indubitable by Karl.R.Gentry et al

in [4]. Although slightly regular functions are referable at complete regular mappings it has y

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been premeditated and patent clear considerably by some authors using topological properties.

In 1947, Choquet [1] indubitable the referableion of a martyr which has been milestone of

developing topology via martyrs. Almost complete the chief concepts of unconcealed topology

possess been prepared to a indubitable distance in martyr referableions by diversified intellectuals.

It is widely

known that in manifold aspects, martyrs are more e ective than a indubitable correspondent concepts

like nets and lters. E.Hatir and Jafari prefaced the expectation of G-regular functions

in [3] and they showed that the concept of public and G-public are recalcitrant of each

other. Dhananjay Mandal and M.N.Mukherjee premeditated the referableion of G-precontinuous

mappings in [2]. Our guard of this monograph is to preface and consider newlightlight concepts namely

slightly G-preregular mapping and slightly G-semipublic mapping. Also, their

characterizations, interrelations and examples are premeditated.

Throughout this monograph, Xstands control a topological boundlessness with no dissociation axioms

assumed original lucidly absorbed. Control a subregular Hof X, the blocking up of Hand the interior

of Hdenoted by Cl ( H) and Int ( H) repectively. The capacity regular of Xdenoted by P(X ) .

The de nitions and results which are used in this monograph of topological and martyr

topological boundlessnesss possess already fascinated some model figure. We reccomplete those de nitions

and basic properties as follows:

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

) is designated slightly regular[4] if there

exists an public regular A, on (X ;F ) such that A f


(B ), control any public regular B,

on (Y ;F 0

) .

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

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

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