Topologies Between Compact and Uniform Convergence on Function Spaces, II

1992 ◽  
Vol 18 (1) ◽  
pp. 176 ◽  
Author(s):  
Kundu ◽  
McCoy ◽  
Raha
Keyword(s):  
Uniform Convergence ◽  
Function Spaces

scholarly journals Topologies between compact and uniform convergence on function spaces

1993 ◽  
Vol 16 (1) ◽  
pp. 101-109 ◽  
Author(s):  
S. Kundu ◽  
R. A. McCoy
Keyword(s):  
Uniform Convergence ◽  
Function Spaces ◽  
Tychonoff Space ◽  
Compact Convergence

This paper studies two topologies on the set of all continuous real-valued functions on a Tychonoff space which lie between the topologies of compact convergence and uniform convergence.

scholarly journals Statistical Convergence in Function Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Agata Caserta ◽  
Giuseppe Di Maio ◽  
Ljubiša D. R. Kočinac
Keyword(s):  
Uniform Convergence ◽  
Statistical Convergence ◽  
Statistical Approach ◽  
Metric Spaces ◽  
Function Spaces ◽  
Strong Uniform Convergence ◽  
Convergence Of Sequences

We study statistical versions of several classical kinds of convergence of sequences of functions between metric spaces (Dini, Arzelà, and Alexandroff) in different function spaces. Also, we discuss a statistical approach to recently introduced notions of strong uniform convergence and exhaustiveness.

scholarly journals The category of uniform convergence spaces is cartesian closed

1976 ◽  
Vol 15 (3) ◽  
pp. 461-465 ◽  
Author(s):  
R.S. Lee
Keyword(s):  
Uniform Convergence ◽  
Function Spaces ◽  
Convergence Spaces ◽  
Cartesian Closedness ◽  
Cartesian Closed ◽  
And Function

This paper first assigns specific uniform convergence structures to the products and function spaces of pairs of uniform convergence spaces, and then establishes a bijection between corresponding sets of morphisms which yields cartesian closedness.

scholarly journals I-Completeness in Function Spaces

2019 ◽  
Vol 74 (1) ◽  
pp. 35-46
Author(s):  
Amar Kumar Banerjee ◽  
Apurba Banerjee
Keyword(s):  
Uniform Convergence ◽  
Topological Structure ◽  
Function Spaces ◽  
Sufficient Condition

Abstract In this paper, we have studied the idea of ideal completeness of function spaces YX with respect to pointwise uniformity and uniformity of uniform convergence. Further, involving topological structure on X,wehaveobtained relationships between the uniformity of uniform convergence on compacta on YX and uniformity of uniform convergence on Y X in terms of I-Cauchy condition and I-convergence of a net. Also, using the notion of a k-space, we have given a sufficient condition for C(X, Y) to be ideal complete with respect to the uniformity of uniform convergence on compacta.

Local Compactness in Set Valued Function Spaces

1976 ◽  
Vol 19 (2) ◽  
pp. 193-198 ◽  
Author(s):  
Saroop K. Kaul
Keyword(s):  
Uniform Convergence ◽  
Uniform Space ◽  
Continuous Functions ◽  
Function Spaces ◽  
Range Space ◽  
Locally Compact ◽  
Local Compactness

Recently Hunsaker and Naimpally [2] have proved: The pointwise closure of an equicontinuous family of point compact relations from a compact T2-space to a locally compact uniform space is locally compact in the topology of uniform convergence. This is a generalization of the same result of Fuller [1] for single valued continuous functions.For a range space which is locally compact normal and uniform theorem B below is an improvement on the result of Hunsaker and Naimpally quoted above [see Remark 3 at the end of this paper].

The Clp-compact-open topology on function spaces

2017 ◽  
Vol 8 (1) ◽  
pp. 31 ◽  
Author(s):  
Ismail Osmano˘glu
Keyword(s):  
Uniform Convergence ◽  
Function Spaces ◽  
Compact Open Topology

In this paper, we introduce (weak) clp-compact-open topology on \(C(X)\) and compare this topology with compact-open topology and the topology of uniform convergence. Then we examine metrizability, completeness and countability properties of the weak clp-compact-open topology on \(C^∗(X)\).

scholarly journals Characterization of pseudocompactness by the topology of uniform convergence on function spaces

1978 ◽  
Vol 26 (2) ◽  
pp. 251-256 ◽  
Author(s):  
R. A. McCoy
Keyword(s):  
Uniform Convergence ◽  
Continuous Functions ◽  
Function Spaces ◽  
Metrizable Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Space Of Continuous Functions ◽  
Tychonoff Space ◽  
Necessary And Sufficient

AbstractIt is shown that a Tychonoff space X is pseudocompact if and only if for every metrizable space Y, all uniformities on Y induce the same topology on the space of continuous functions from X into Y. Also for certain pairs of spaces X and Y, a necessary and sufficient condition is established in order that all uniformities on Y induce the same topology on the space of continuous functions from X into Y.

scholarly journals Bornologies and bitopological function spaces

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1345-1349 ◽  
Author(s):  
Selma Özçağ
Keyword(s):  
Uniform Convergence ◽  
Metric Spaces ◽  
Function Spaces ◽  
Uniform Topology ◽  
Selection Principles ◽  
Strong Uniform Convergence

The aim of this paper is to study certain closure-type properties of function spaces over metric spaces endowed with two topologies: the topology of uniform convergence on a bornology and the topology of strong uniform convergence on a bornology. The study of function spaces with the strong uniform topology on a bornology was initiated by G. Beer and S. Levi in 2009, and then continued by several authors: A. Caserta, G. Di Maio and L'. Hol? in 2010, A. Caserta, G. Di Maio, Lj.D.R. Kocinac in 2012. Properties that we consider in this paper are defined in terms of selection principles.

scholarly journals Quasi-uniform convergence topologies on function spaces- Revisited

2017 ◽  
Vol 18 (2) ◽  
pp. 301
Author(s):  
Wafa Khalaf Alqurash ◽  
Liaqat Ali Khan
Keyword(s):  
Topological Space ◽  
Uniform Convergence ◽  
Uniform Space ◽  
Continuous Functions ◽  
Function Spaces

Let X and Y be topological space and F(X,Y) the set of all functions from X into Y. We study various quasi-uniform convergence topologies U_{A} (A⊆P(X)) on F(X,Y) and their comparison in the setting of Y a quasi-uniform space. Further, we study U_{A}-closedness and right K-completeness properties of certain subspaces of generalized continuous functions in F(X,Y) in the case of Y a locally symmetric quasi-uniform space or a locally uniform space.

scholarly journals Set-open topologies on function spaces

2018 ◽  
Vol 19 (1) ◽  
pp. 55
Author(s):  
Wafa Khalaf Alqurashi ◽  
Liaqat Ali Khan ◽  
Alexander V. Osipov
Keyword(s):  
Topological Space ◽  
Uniform Convergence ◽  
Uniform Space ◽  
Continuous Functions ◽  
Function Spaces ◽  
Topological Spaces ◽  
General Topological Space

<p>Let X and Y be topological spaces, F(X,Y) the set of all functions from X into Y and C(X,Y) the set of all continuous functions in F(X,Y). We study various set-open topologies tλ (λ ⊆ P(X)) on F(X,Y) and consider their existence, comparison and coincidence in the setting of Y a general topological space as well as for Y = R. Further, we consider the parallel notion of quasi-uniform convergence topologies Uλ (λ ⊆ P(X)) on F(X,Y) to discuss Uλ-closedness and right Uλ-K-completeness properties of a certain subspace of F(X,Y) in the case of Y a locally symmetric quasi-uniform space. We include some counter-examples to justify our comments.</p>

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