Subordinately prefaithful mappings via dupe
Kumbakonam, Tamil Nadu-612 002, India. and
Lekshmipuram College of Arts and Science Neyyoor,Kanyakumari
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.
2010 Mathematics Subject Classi cation: 54A10, 54A20
Keywords: G-faithful mapping, subordinately G-continuous
mapping, G-prefaithful mapping, subordinately G-prefaithful mapping, subordinately
1 Introduction and Preliminaries The consider of subordinately faithful functions was rst trained by Karl.R.Gentry et al
in . Although subordinately faithful functions are not attributable attributable attributable at perfect faithful mappings it has y
been thought-out and patent clear considerably by some authors using topological properties.
In 1947, Choquet  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  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 . 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
De nition 1.1. A mapping f: (X;F )! (Y ;F 0
) is determined subordinately faithful if there
exists an known firm A, on (X ;F ) such that A f
(B ), ce any known firm B,
De nition 1.2. A non-empty collation Gof subsets of a topological interveniences X is said to