ON LINEAR TOPOLOGICAL CLASSIFICATION OF SPACES OF CONTINUOUS FUNCTIONS IN THE TOPOLOGY OF POINTWISE CONVERGENCE

1991 ◽  
Vol 70 (1) ◽  
pp. 129-142 ◽  
Author(s):  
A V Arkhangel'skiĭ
Keyword(s):  
Pointwise Convergence ◽  
Continuous Functions ◽  
Topological Classification ◽  
Spaces Of Continuous Functions ◽  
Topology Of Pointwise Convergence

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.

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.

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>

scholarly journals Classification of spaces of continuous functions on ordinals

2018 ◽  
Vol 59 (3) ◽  
pp. 365-370
Author(s):  
 Genze Leonid V. ◽  
Gul'ko Sergei P. ◽  
Khmyleva Tat'ana E.
Keyword(s):  
Continuous Functions ◽  
Spaces Of Continuous Functions
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