Somewhat precontinuous mappings via grill Essay

Subordinately prefaithful mappings via dupe

A. Swaminathany

Department of Mathematics

Government Arts College(Autonomous)

Kumbakonam, Tamil Nadu-612 002, India. and

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M. Sankari

Department of Mathematics

Lekshmipuram College of Arts and Science Neyyoor,Kanyakumari

Tamil Nadu-629 802, India.

Abstract

This period begins the concepts of subordinately G-prefaithful mapping and

subordinately G-preknown mappings. Using these not attributable attributableions, some examples and lacking interesting

properties of those mappings are discussed by media of dupe topological interveniences.

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2010 Mathematics Subject Classi cation: 54A10, 54A20

Keywords: G-faithful mapping, subordinately G-continuous

mapping, G-prefaithful mapping, subordinately G-prefaithful mapping, subordinately

G -preknown mapping. G-predense firm.

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

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

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1

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2

been thought-out and patent clear considerably by some authors using topological properties.

In 1947, Choquet [1] orderly the not attributable attributableion of a dupe which has been milestone of

developing topology via dupes. Almost perfect the prominent concepts of unconcealed topology

enjoy been adept to a infallible quantity in dupe not attributable attributableions by sundry intellectuals.

It is widely

known that in multifarious aspects, dupes are past e ective than a infallible congruous concepts

like nets and lters. E.Hatir and Jafari begind the idea of G-faithful functions

in [3] and they showed that the concept of known and G-known are rebellious of each

other. Dhananjay Mandal and M.N.Mukherjee thought-out the not attributable attributableion of G-precontinuous

mappings in [2]. Our incline of this pamphlet is to begin and consider upstart concepts namely

subordinately G-prefaithful mapping and subordinately G-semiknown mapping. Also, their

characterizations, interrelations and examples are thought-out.

Throughout this pamphlet, Xstands ce a topological intervenience with no dissociation axioms

assumed intrinsic plainly dedicated. Ce a subfirm Hof X, the imperviousness of Hand the interior

of Hdenoted by Cl ( H) and Int ( H) repectively. The controlce firm of Xdenoted by P(X ) .

The de nitions and results which are used in this pamphlet relating topological and dupe

topological interveniences enjoy already enslaved some trutination fashion. We recperfect those de nitions

and basic properties as follows:

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

) is determined subordinately faithful[4] if there

exists an known firm A, on (X ;F ) such that A f

1

(B ), ce any known firm B,

on (Y ;F 0

) .

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

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

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