$\pi g^* \beta$-CONTINUOUS FUNCTION IN TOPOLOGICAL SPACES

2020 ◽  
Vol 9 (7) ◽  
pp. 5251-5255
Author(s):  
S. Savitha ◽  
S. Gomathi
Keyword(s):  
Continuous Function ◽  
Topological 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.

scholarly journals ‎INSERTION OF A CONTRA-CONTINUOUS FUNCTION BETWEEN TWO ‎‎COMPARABLE CONTRA-$\alpha-$CONTINUOUS (CONTRA-$C-$CONTINUOUS) FUNCTIONS

2019 ◽  
pp. 13
Author(s):  
Majid Mirmiran ◽  
Binesh Naderi
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

‎A necessary and sufficient condition in terms of lower cut sets ‎are given for the insertion of a contra-continuous function ‎between two comparable real-valued functions on such topological ‎spaces that kernel of sets are open‎. 

scholarly journals On subsequential limit points of a sequence of iterates. II

1985 ◽  
Vol 38 (1) ◽  
pp. 118-129
Author(s):  
M. Maiti ◽  
A. C. Babu
Keyword(s):  
Continuous Function ◽  
Distance Function ◽  
Metric Space ◽  
Product Space ◽  
Topological Spaces ◽  
Limit Points ◽  
Cluster Points

AbstractJ. B. Diaz and F. T. Metcalf established some results concerning the structure of the set of cluster points of a sequence of iterates of a continuous self-map of a metric space. In this paper it is shown that their conclusions remain valid if the distance function in their inequality is replaced by a continuous function on the product space. Then this idea is extended to some other mappings and to uniform and general topological spaces.

scholarly journals Almost-periodicity in linear topological spaces and applications to abstract differential equations

1984 ◽  
Vol 7 (3) ◽  
pp. 529-540 ◽  
Author(s):  
Gaston Mandata N'Guerekata
Keyword(s):  
Continuous Function ◽  
Real Line ◽  
Locally Convex Space ◽  
Topological Spaces ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Fréchet Spaces ◽  
Abstract Differential Equations ◽  
T Tau ◽  
Locally Convex

LetEbe a complete locally convex space (l.c.s.) andf:R→Ea continuous function; thenfis said to be almost-periodic (a.p.) if, for every neighbourhood (of the origin inE)U, there existsℓ=ℓ(U)>0such that every interval[a,a+ℓ]of the real line contains at least oneτpoint such thatf(t+τ)−f(t)∈Ufor everyt∈R. We prove in this paper many useful properties of a.p. functions in l.c.s, and give Bochner's criteria in Fréchet spaces.

scholarly journals Fine Fuzzy sp Closed Sets in Fine Fuzzy Topological Spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 1306-1313
Keyword(s):  
Continuous Function ◽  
Topological Space ◽  
Inverse Image ◽  
Continuous Functions ◽  
Topological Spaces ◽  
The Novel ◽  
Closed Set ◽  
Closed Sets ◽  
Fuzzy Topological Space ◽  
Fuzzy Topological Spaces

The main view of this article is the extended version of the fine topological space to the novel kind of space say fine fuzzy topological space which is developed by the notion called collection of quasi coincident of fuzzy sets. In this connection, fine fuzzy closed sets are introduced and studied some features on it. Further, the relationship between fine fuzzy closed sets with certain types of fine fuzzy closed sets are investigated and their converses need not be true are elucidated with necessary examples. Fine fuzzy continuous function is defined as the inverse image of fine fuzzy closed set is fine fuzzy closed and its interrelations with other types of fine fuzzy continuous functions are obtained. The reverse implication need not be true is proven with examples. Finally, the applications of fine fuzzy continuous function are explained by using the composition.

scholarly journals SOME WEAKER FORMS OF SMOOTH FUZZY CONTINUOUS FUNCTIONS

2017 ◽  
Vol 36 (2) ◽  
Author(s):  
Chandran Kalaivani ◽  
Rajakumar Roopkumar
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Proper Functions ◽  
Fuzzy Topological Spaces ◽  
Equivalent Conditions

In this paper we introduce various notions of continuous fuzzy proper functions by using the existing notions of fuzzy closure and fuzzy interior operators like 𝑅𝜏𝑟-closure, 𝑅𝜏𝑟-interior, etc., and present all possible relations among these types of continuities. Next, we introduce the concepts of α-quasi-coincidence, 𝑞𝛼𝑟-pre-neighborhood, 𝑞𝛼𝑟-pre-clo-sure and 𝑞𝛼𝑟- pre-continuous function in smooth fuzzy topological spaces and investigate the equivalent conditions of 𝑞𝛼𝑟- pre-continuity.

scholarly journals A GENERALIZATION OF SIERPINSKI THEOREM ON UNIQUE DETERMINING OF A SEPARATELY CONTINUOUS FUNCTION

2021 ◽  
Vol 9 (1) ◽  
pp. 250-263
Author(s):  
V. Mykhaylyuk ◽  
O. Karlova
Keyword(s):  
Continuous Function ◽  
Topological Space ◽  
Dense Subset ◽  
Continuous Functions ◽  
Baire Space ◽  
Regular Space ◽  
Topological Spaces ◽  
Infinite Cardinal ◽  
Urysohn Space ◽  
Completely Regular

In 1932 Sierpi\'nski proved that every real-valued separately continuous function defined on the plane $\mathbb R^2$ is determined uniquely on any everywhere dense subset of $\mathbb R^2$. Namely, if two separately continuous functions coincide of an everywhere dense subset of $\mathbb R^2$, then they are equal at each point of the plane. Piotrowski and Wingler showed that above-mentioned results can be transferred to maps with values in completely regular spaces. They proved that if every separately continuous function $f:X\times Y\to \mathbb R$ is feebly continuous, then for every completely regular space $Z$ every separately continuous map defined on $X\times Y$ with values in $Z$ is determined uniquely on everywhere dense subset of $X\times Y$. Henriksen and Woods proved that for an infinite cardinal $\aleph$, an $\aleph^+$-Baire space $X$ and a topological space $Y$ with countable $\pi$-character every separately continuous function $f:X\times Y\to \mathbb R$ is also determined uniquely on everywhere dense subset of $X\times Y$. Later, Mykhaylyuk proved the same result for a Baire space $X$, a topological space $Y$ with countable $\pi$-character and Urysohn space $Z$. Moreover, it is natural to consider weaker conditions than separate continuity. The results in this direction were obtained by Volodymyr Maslyuchenko and Filipchuk. They proved that if $X$ is a Baire space, $Y$ is a topological space with countable $\pi$-character, $Z$ is Urysohn space, $A\subseteq X\times Y$ is everywhere dense set, $f:X\times Y\to Z$ and $g:X\times Y\to Z$ are weakly horizontally quasi-continuous, continuous with respect to the second variable, equi-feebly continuous wuth respect to the first one and such that $f|_A=g|_A$, then $f=g$. In this paper we generalize all of the results mentioned above. Moreover, we analize classes of topological spaces wich are favorable for Sierpi\'nsi-type theorems.

scholarly journals More Functions Associated with Neutrosophic gsα*- Closed Sets in Neutrosophic Topological Spaces

2021 ◽  
Author(s):  
P. Anbarasi Rodrigo ◽  
S. Maheswari
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
Topological Spaces ◽  
Closed Sets

The concept of neutrosophic continuous function was very first introduced by A.A. Salama et al. The main aim of this paper is to introduce a new concept of Neutrosophic continuous function namely Strongly Neutrosophic gsα* - continuous functions, Perfectly Neutrosophic gsα* - continuous functions and Totally Neutrosophic gsα* - continuous functions in Neutrosophic topological spaces. These concepts are derived from strongly generalized neutrosophic continuous function and perfectly generalized neutrosophic continuous function. Several interesting properties and characterizations are derived and compared with already existing neutrosophic functions.

scholarly journals Neutrosophic e-Continuous Maps and Neutrosophic e-Irresolute Maps

2021 ◽  
Vol 12 (1S) ◽  
pp. 369-375
Author(s):  
A. Vadivel Et. al.
Keyword(s):  
Continuous Function ◽  
Topological Spaces ◽  
Properties And Characterization ◽  
Continuous Maps

Aim of this present paper is to introduce and investigate new kind of neutrosophic continuous function called neutrosophic econtinuous maps in neutrosophic topological spaces and also relate with their near continuous maps. Also, a new irresolute map called neutrosophic e-irresolute maps in neutrosophic topological spaces is introduced. Further, discussed about some properties and characterization of neutrosophic e-irresolute maps in neutrosophic topological spaces.

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