scholarly journals Contra-ω-Continuous and Almost Contra-ω-Continuous

2007 ◽  
Vol 2007 ◽  
pp. 1-13 ◽  
Author(s):  
Ahmad Al-Omari ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
New Class

The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion ofω-open sets in topological space to present and study a new class of called almost contraω-continuous functions as a new generalization of contra continuity.

scholarly journals gs Continuous Function in Topological Space

ISRN Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
S. Pious Missier ◽  
Vijilius Helena Raj
Keyword(s):  
Continuous Function ◽  
Topological Space ◽  
Continuous Functions ◽  
Topological Spaces ◽  
New Class ◽  
Properties And Characterization

We introduce the different notions of a new class of continuous functions called generalized semi Lambda (gs) continuous function in topological spaces. Its properties and characterization are also discussed.

scholarly journals Soft ωp-Open Sets and Soft ωp-Continuity in Soft Topological Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2632
Author(s):  
Samer Al Ghour
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Strong Form ◽  
Topological Spaces ◽  
New Class ◽  
Soft Topology ◽  
Dense Sets ◽  
Soft Topological Space

We define soft ωp-openness as a strong form of soft pre-openness. We prove that the class of soft ωp-open sets is closed under soft union and do not form a soft topology, in general. We prove that soft ωp-open sets which are countable are soft open sets, and we prove that soft pre-open sets which are soft ω-open sets are soft ωp-open sets. In addition, we give a decomposition of soft ωp-open sets in terms of soft open sets and soft ω-dense sets. Moreover, we study the correspondence between the soft topology soft ωp-open sets in a soft topological space and its generated topological spaces, and vice versa. In addition to these, we define soft ωp-continuous functions as a new class of soft mappings which lies strictly between the classes of soft continuous functions and soft pre-continuous functions. We introduce several characterizations for soft pre-continuity and soft ωp-continuity. Finally, we study several relationships related to soft ωp-continuity.

Real Functions, Covers and Bornologies

2021 ◽  
Vol 78 (1) ◽  
pp. 199-214
Author(s):  
Lev Bukovský
Keyword(s):  
Topological Space ◽  
Pointwise Convergence ◽  
Continuous Functions ◽  
Upper Semicontinuous ◽  
Upper Semicontinuous Functions ◽  
Covering Properties ◽  
Real Functions ◽  
Topology Of Pointwise Convergence ◽  
Semicontinuous Functions

Abstract The paper tries to survey the recent results about relationships between covering properties of a topological space X and the space USC(X) of upper semicontinuous functions on X with the topology of pointwise convergence. Dealing with properties of continuous functions C(X), we need shrinkable covers. The results are extended for A-measurable and upper A-semimeasurable functions where A is a family of subsets of X. Similar results for covers respecting a bornology and spaces USC(X) or C(X) endowed by a topology defined by using the bornology are presented. Some of them seem to be new.

scholarly journals New approach of ideal topological generalized closed sets

2013 ◽  
Vol 31 (2) ◽  
pp. 191
Author(s):  
Chinnapazham Santhini ◽  
M. Lellis Thivagar
Keyword(s):  
Continuous Functions ◽  
New Approach ◽  
Closed Sets ◽  
New Class

In this paper,we introduce and investigate the notions of Iˆω -closed sets andI ˆω -continuous functions,maximal Iˆω -closed sets and maximal Iˆω -continuous functionsin ideal topological spaces.We also introduce a new class of spaces calledMTˆω -spaces.

scholarly journals A note on weakly θ-continuous functions

1989 ◽  
Vol 12 (1) ◽  
pp. 9-13 ◽  
Author(s):  
M. Mrševic ◽  
I. L. Reilly
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
Topological Spaces ◽  
New Class ◽  
Weakly Continuous ◽  
Class Of Functions

Recently a new class of functions between topological spaces, called weaklyθ-continuous functions, has been introduced and studied. In this paper we show how an appropriate change of topology on the domain of a weaklyθ-continuous function reduces it to a weakly continuous function. This paper examines some of the consequences of this result.

Order continuous measures

1964 ◽  
Vol 60 (2) ◽  
pp. 205-207 ◽  
Author(s):  
G. T. Roberts
Keyword(s):  
Topological Space ◽  
Linear Form ◽  
Vector Lattice ◽  
Measure Zero ◽  
Continuous Functions ◽  
Order Convergence ◽  
Locally Compact ◽  
Compact Topological Space ◽  
Continuous Measures ◽  
Order Continuous

1. Objective. It is possible to define order convergence on the vector lattice of all continuous functions of compact support on a locally compact topological space. Every measure is a linear form on this vector lattice. The object of this paper is to prove that a measure is such that every set of the first category of Baire has measure zero if and only if the measure is a linear form which is continuous in the order convergence.

scholarly journals On a topology between Tα and Tγα

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3209-3221
Author(s):  
Dimitrije Andrijevic
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Closure Operators ◽  
New Class ◽  
Necessary And Sufficient

Using the topology T in a topological space (X,T), a new class of generalized open sets called ?-preopen sets, is introduced and studied. This class generates a new topology Tg which is larger than T? and smaller than T??. By means of the corresponding interior and closure operators, among other results, necessary and sufficient conditions are given for Tg to coincide with T? , T? or T??.

scholarly journals δ-perfectly continuous functions

2009 ◽  
Vol 42 (1) ◽  
Author(s):  
J. K. Kohli ◽  
D. Singh
Keyword(s):  
Continuous Functions ◽  
New Class ◽  
Class Of Functions

AbstractA new class of functions called ‘

Restrictive Semigroups of Continuous Functions on 0-Dimensional Spaces

1972 ◽  
Vol 24 (4) ◽  
pp. 598-611 ◽  
Author(s):  
Robert D. Hofer
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Analogous Problem

Let X be a topological space and Y a nonempty subspace of X. Γ(X, Y) denotes the semigroup under composition of all closed self maps of X which carry Y into Y, and is referred to as a restrictive semigroup of closed functions. Similarly, S(X, Y) is the analogous semigroup of continuous selfmaps of X, and is referred to as a restrictive semigroup of continuous functions. It is immediate that each homeomorphism from X onto U which carries the subspace Y of X onto the subspace V of U induces an isomorphism between Γ(X, Y) and Γ(U, V), and also an isomorphism between S(X, Y) and S(U, V). Indeed, one need only map f onto h o f o h-1. An isomorphism of this form is called representable. In [5, Theorem (3.1), p. 1223] it was shown that in most cases, each isomorphism from Γ(X, Y) onto Γ(U, V) is representable. The analogous problem was discussed for the semigroup S(X, Y) and it was pointed out by means of an example that one could not hope to obtain the same result for these semigroups without some further restrictions.

scholarly journals Completion of lattices of semi-continuous functions

1978 ◽  
Vol 26 (4) ◽  
pp. 453-464 ◽  
Author(s):  
John August ◽  
Charles Byrne
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Distributive Lattices ◽  
Normal Completion ◽  
Bitopological Spaces

AbstractIf U and V are toplogies on an abstract set x, then the triple (X, U, V) is a bitopologica space. Using the theorem of Priestley on the representation of distributive lattices, results of Dilworth concerning the normal completion of the lattice of bounded, continuous, realvalued functions on a topological space are extended to include the lattice of bounded, semi-continuous, real-valued functions on certain bitopological spaces. The distributivity of certain lattices is investigated, and the theorem of Funayama on distributive normal completions is generalized.

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