scholarly journals SYMMETRICALLY CONTINUOUS FUNCTIONS ON VARIOUS SUBSETS OF THE REAL LINE

1999 ◽  
Vol 25 (2) ◽  
pp. 547 ◽  
Author(s):  
Szyszkowski
Keyword(s):  
Real Line ◽  
Continuous Functions ◽  
The Real ◽  
Symmetrically Continuous Functions

scholarly journals Remarks on uniformly symmetrically continuous functions

2016 ◽  
Vol 09 (03) ◽  
pp. 1650069
Author(s):  
Tammatada Khemaratchatakumthorn ◽  
Prapanpong Pongsriiam
Keyword(s):  
Real Line ◽  
Nonempty Subset ◽  
Continuous Functions ◽  
The Real ◽  
Definition Of ◽  
Symmetrically Continuous Functions ◽  
Uniformly Continuous

We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of symmetrically continuous functions and uniformly continuous functions. We obtain some characterizations of uniformly symmetrically continuous functions. Several examples are also given.

Statistical σ approximation to Bögel-type continuous functions

2011 ◽  
Vol 48 (4) ◽  
pp. 475-488 ◽  
Author(s):  
Sevda Karakuş ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Result ◽  
The Real

In this paper, using the concept of statistical σ-convergence which is stronger than the statistical convergence, we obtain a statistical σ-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. Then, we construct an example such that our new approximation result works but its classical and statistical cases do not work. Also we compute the rate of statistical σ-convergence of sequence of positive linear operators.

A non-constant invariant function for certain ergodic flows

2008 ◽  
Vol 28 (3) ◽  
pp. 1031-1035
Author(s):  
SOL SCHWARTZMAN
Keyword(s):  
Vector Space ◽  
Real Line ◽  
Differentiable Manifold ◽  
Invariant Function ◽  
Continuous Functions ◽  
The Real ◽  
Almost All ◽  
Uniformly Continuous

AbstractLet U be the vector space of uniformly continuous real-valued functions on the real line $\mathbb {R}$ and let U0 denote the subspace of U consisting of all bounded uniformly continuous functions. If X is a compact differentiable manifold and we are given a flow on X, then we associate with the flow a function F:X→H1(X,U/U0) that is invariant under the flow. We give examples for which the flow on X is ergodic but there is no λ∈H1(X,U/U0) such that F(p)=λ for almost all points p.

scholarly journals A category analogue of the generalization of Lebesgue density topology

2009 ◽  
Vol 42 (1) ◽  
pp. 11-25
Author(s):  
Wojciech Wojdowski
Keyword(s):  
Real Line ◽  
Continuous Functions ◽  
Density Point ◽  
Density Topology ◽  
The Real ◽  
Lebesgue Density ◽  
Real Anal

Abstract . A notion of AI -topology, a generalization of Wilczy´nski’s I-density topology (see [Wilczy´nski, W.: A generalization of the density topology, Real. Anal. Exchange 8 (1982-1983), 16-20] is introduced. The notion is based on his reformulation of the definition od Lebesgue density point. We consider a category version of the topology, which is a category analogue of the notion of an Ad- -density topology on the real line given in [Wojdowski, W.: A generalization ofdensity topology, Real. Anal. Exchange 32 (2006/2007), 1-10]. We also discuss the properties of continuous functions with respect to the topology.

Note on a Subalgebra of C(X)

1972 ◽  
Vol 15 (4) ◽  
pp. 607-608 ◽  
Author(s):  
L. D. Nel ◽  
D. Riordan
Keyword(s):  
Real Line ◽  
Maximal Ideal ◽  
Residue Class ◽  
Continuous Functions ◽  
The Real ◽  
Residue Class Ring ◽  
Class Ring ◽  
Bounded Continuous Functions

C(X) (resp. C*(X)) will denote as usual the ring of all (resp. all bounded) continuous functions into the real line R. Define C#(X) to consist of all f∊C(X) whose image M(f) in the residue class ring C(X)jM is real for every maximal ideal M in C(X). Then C# shares with C* the property of being an intrinsically determined subalgebra of C. Then C* shares with C* the property of being an intrinsically determined subalgebra of C. The compactification corresponding to C# (as uniformity determining subalgebra of C*) is thus also an intrinsically determined one. We show that this compactification is well known and "natural" in the cases of several elementary spaces X.

On Vector Lattice-Valued Measures

1965 ◽  
Vol 8 (4) ◽  
pp. 499-504
Author(s):  
R. Hrycay
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Linear Functional ◽  
Vector Lattice ◽  
Continuous Functions ◽  
The Real ◽  
Measure Function ◽  
Complex Valued

E. Hewitt [1] used the Daniell approach to define a real-valued measure function on a σ-algebra of the real line. He began by defining an arbitrary non-negative linear functional I on L∞ ∞(R), (the space of all complex-valued continuous functions on the real line R which vanish off some compact subset of R).

scholarly journals The set of points of discontinuity of ℐ-approximately continuous functions

2010 ◽  
Vol 43 (3) ◽  
Author(s):  
Władysław Wilczyński
Keyword(s):  
Real Line ◽  
Continuous Functions ◽  
Natural Topology ◽  
The Real ◽  
Set Of Points ◽  
Points Of Discontinuity

AbstractThe paper presents the characterization of the set of points of discontinuity (with respect to the natural topology on the real line) of an

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