scholarly journals Density topology and pointwise convergence

2003 ◽  
Vol 4 (2) ◽  
pp. 509 ◽  
Author(s):  
Wladyslaw Wilczynski
Keyword(s):  
Pointwise Convergence ◽  
Continuous Functions ◽  
Density Topology ◽  
Topology Of Pointwise Convergence

<p>We shall show that the space of all approximately continuous functions with the topology of pointwise convergence is not homeomorphic to its category analogue.</p>

Real Functions, Covers and Bornologies

2021 ◽  
Vol 78 (1) ◽  
pp. 199-214
Author(s):  
Lev Bukovský
Keyword(s):  
Topological Space ◽  
Pointwise Convergence ◽  
Continuous Functions ◽  
Upper Semicontinuous ◽  
Upper Semicontinuous Functions ◽  
Covering Properties ◽  
Real Functions ◽  
Topology Of Pointwise Convergence ◽  
Semicontinuous Functions

Abstract The paper tries to survey the recent results about relationships between covering properties of a topological space X and the space USC(X) of upper semicontinuous functions on X with the topology of pointwise convergence. Dealing with properties of continuous functions C(X), we need shrinkable covers. The results are extended for A-measurable and upper A-semimeasurable functions where A is a family of subsets of X. Similar results for covers respecting a bornology and spaces USC(X) or C(X) endowed by a topology defined by using the bornology are presented. Some of them seem to be new.

LΣ(≤ ω)-spaces and spaces of continuous functions

2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Israel Lara ◽  
Oleg Okunev
Keyword(s):  
Compact Space ◽  
Pointwise Convergence ◽  
Continuous Functions ◽  
Spaces Of Continuous Functions ◽  
Topology Of Pointwise Convergence

AbstractWe present a few results and problems related to spaces of continuous functions with the topology of pointwise convergence and the classes of LΣ(≤ ω)-spaces; in particular, we prove that every Gul’ko compact space of cardinality less or equal to $$ \mathfrak{c} $$ is an LΣ(≤ ω)-space.

scholarly journals On linear continuous operators on C_p-spaces

2021 ◽  
Vol 21 (1) ◽  
pp. 45-50
Author(s):  
A.P. Devyatkov ◽  
◽  
S.D. Shalaginov ◽  
Keyword(s):  
Linear Functional ◽  
Pointwise Convergence ◽  
Continuous Operator ◽  
Continuous Functions ◽  
Linear Continuous Operator ◽  
Continuous Linear ◽  
Space Of Continuous Functions ◽  
Continuous Linear Functional ◽  
Topology Of Pointwise Convergence ◽  
Continuous Operators

The paper describes the structure of a linear continuous operator on the space of continuous functions in the topology of pointwise convergence. The corresponding theorem is a generalization of A.V.Arkhangel'skii's theorem on the general form of a continuous linear functional on such spaces.

scholarly journals Selection principles and games in bitopological function spaces

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4535-4540
Author(s):  
Daniil Lyakhovets ◽  
Alexander Osipov
Keyword(s):  
Pointwise Convergence ◽  
Continuous Functions ◽  
Function Spaces ◽  
Compact Open Topology ◽  
Bitopological Space ◽  
Tychonoff Space ◽  
Selection Principles ◽  
Topology Of Pointwise Convergence ◽  
Selective Separability

For a Tychonoff space X, we denote by (C(X), ?k ?p) the bitopological space of all real-valued continuous functions on X, where ?k is the compact-open topology and ?p is the topology of pointwise convergence. In the papers [6, 7, 13] variations of selective separability and tightness in (C(X),?k,?p) were investigated. In this paper we continue to study the selective properties and the corresponding topological games in the space (C(X),?k,?p).

scholarly journals k-space function spaces

1980 ◽  
Vol 3 (4) ◽  
pp. 701-711 ◽  
Author(s):  
R. A. McCoy
Keyword(s):  
Pointwise Convergence ◽  
Continuous Functions ◽  
Function Spaces ◽  
Space Function ◽  
Topology Of Pointwise Convergence ◽  
Space Property

A study is made of the properties onXwhich characterize whenCπ(X)is ak-space, whereCπ(X)is the space of real-valued continuous functions onXhaving the topology of pointwise convergence. Other properties related to thek-space property are also considered.

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