On O’Malley preponderantly continuous functions

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
Stanisław Kowalczyk
Keyword(s):  
Continuous Functions ◽  
Algebraic Properties ◽  
Satisfying Property

AbstractIn the paper some algebraic properties of functions which are preponderantly continuous in O'Malley sense and functions satisfying property

scholarly journals On generalizations of C*-embedding for wallman rings

1978 ◽  
Vol 25 (2) ◽  
pp. 215-229 ◽  
Author(s):  
H. L. Bentley ◽  
B. J. Taylor
Keyword(s):  
Topological Space ◽  
Continuous Functions ◽  
Topological Properties ◽  
Zero Sets ◽  
Algebraic Properties

AbstractBiles (1970) has called a subring A of the ring C(X), of all real valued continuous functions on a topological space X, a Wallman ring on X whenever Z(A), the zero sets of functions belonging to A, forms a normal base on X in the sense of Frink (1964). Previously, we have related algebraic properties of a Wallman ring A to topological properties of the Wallman compactification w(Z(A)) of X determined by the normal base Z(A). Here we introduce two different generalizations of the concept of “a C*-embedded subset” and study relationships between these and topological (respectively, algebraic) properties of w(Z(A)) (respectively, A).

scholarly journals Graph theoretic representation of rings of continuous functions

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3417-3428
Author(s):  
Bedanta Bose ◽  
Angsuman Das
Keyword(s):  
Continuous Functions ◽  
Topological Spaces ◽  
Graph Structure ◽  
Zero Set ◽  
Tychonoff Space ◽  
Graph Theoretic ◽  
Maximal Ideals ◽  
Set Intersection ◽  
Algebraic Properties ◽  
Relationship Of

In this paper, we introduce a graph structure, called zero-set intersection graph ?(C(X)), on the ring of real valued continuous functions, C(X), on a Tychonoff space X. We show that the graph is connected and triangulated. We also study the inter-relationship of cliques of ?(C(X)) and ideals in C(X) which helps to characterize the structure of maximal cliques of ?(C(X)) by different kind of maximal ideals of C(X). We show that there are at least 2c many different maximal cliques which are never graph isomorphic to each other. Furthermore, we study the neighbourhood properties of a vertex and show its connection with the topology of X and algebraic properties of C(X). Finally, it is shown that two graphs are isomorphic if and only if the corresponding rings are isomorphic if and only if the corresponding topologies are homeomorphic either for first countable topological spaces or for realcompact topological spaces.

DITKIN CONDITIONS

2017 ◽  
Vol 60 (1) ◽  
pp. 153-163
Author(s):  
AZADEH NIKOU ◽  
ANTHONY G. O'FARRELL
Keyword(s):  
Banach Algebra ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Commutative Banach Algebra ◽  
Algebraic Properties ◽  
The Relationship

AbstractThis paper is about the connection between certain Banach-algebraic properties of a commutative Banach algebra E with unit and the associated commutative Banach algebra C(X, E) of all continuous functions from a compact Hausdorff space X into E. The properties concern Ditkin's condition and bounded relative units. We show that these properties are shared by E and C(X, E). We also consider the relationship between these properties in the algebras E, B and $\~{B}$ that appear in the so-called admissible quadruples (X, E, B, $\~{B}$).

scholarly journals Continuous Functions in Hashimoto Topologies and Their Algebraic Properties

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Artur Bartoszewicz ◽  
Małgorzata Filipczak ◽  
Małgorzata Terepeta
Keyword(s):  
Continuous Functions ◽  
Usual Sense ◽  
Free Algebras ◽  
Natural Topology ◽  
Algebraic Properties

AbstractIn the paper we consider the Hashimoto topologies on the interval $$[0,1]$$ [ 0 , 1 ] as well as on $$\mathbb {R}$$ R , which are connected with the natural topology on $$\mathbb {R}$$ R and with some important and well known $$\sigma $$ σ -ideals in $$\mathcal {P}(\mathbb {R})$$ P ( R ) . We study the families of continuous functions $$f:[0,1]\rightarrow \mathbb {R}$$ f : [ 0 , 1 ] → R with respect to the same Hashimoto topology $$\mathcal {H}(\mathcal {I})$$ H ( I ) (connected with the $$\sigma $$ σ -ideal $$\mathcal {I}$$ I ) on the domain and on the range of the considered functions. We show that inside common parts and differences of some such families we can find large ($$\mathfrak {c}$$ c -generated) free algebras. Some of constructed algebras appear dense in the algebra of the functions which are continuous in the usual sense.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

Almost Somewhat Near Continuity and Near Regularity

2021 ◽  
Vol 7 (1) ◽  
pp. 88-99
Author(s):  
Zanyar A. Ameen
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
One To One ◽  
Nearly Continuous

AbstractThe notions of almost somewhat near continuity of functions and near regularity of spaces are introduced. Some properties of almost somewhat nearly continuous functions and their connections are studied. At the end, it is shown that a one-to-one almost somewhat nearly continuous function f from a space X onto a space Y is somewhat nearly continuous if and only if the range of f is nearly regular.

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