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 \(C^∗(X)\).

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 Quasi-pseudometrizability of the point open ordered spaces and the compact open ordered spaces

2001 ◽  
Vol 26 (7) ◽  
pp. 385-392 ◽  
Author(s):  
Koena Rufus Nailana
Keyword(s):  
Function Spaces ◽  
Compact Open Topology

We determine conditions for quasi-pseudometrizability of the point open ordered spaces and the compact open ordered spaces. This generalizes the results on metrizability of the point open topology and the compact open topology for function spaces. We also study conditions for complete quasi-pseudometrizability.

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 Closure properties of function spaces

2003 ◽  
Vol 4 (2) ◽  
pp. 255 ◽  
Author(s):  
Ljubisa D.R. Kocinac
Keyword(s):  
Function Spaces ◽  
Compact Open Topology ◽  
Closure Properties ◽  
Tychonoff Space

<p>In this paper we investigate some closure properties of the space Ck(X) of continuous real-valued functions on a Tychonoff space X endowed with the compact-open topology.</p>

scholarly journals Sequential properties of function spaces with the compact-open topology

2011 ◽  
Vol 158 (3) ◽  
pp. 387-391 ◽  
Author(s):  
Gary Gruenhage ◽  
Boaz Tsaban ◽  
Lyubomyr Zdomskyy
Keyword(s):  
Function Spaces ◽  
Compact Open Topology

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.

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