quasicontinuous functions
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Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 911-917
Author(s):  
Lubica Holá ◽  
Dusan Holý

Let X be a Hausdorff topological space, Q(X,R) be the space of all quasicontinuous functions on X with values in R and ?UC be the topology of uniform convergence on compacta. If X is hemicompact, then (Q(X,R), ?UC) is metrizable and thus many cardinal invariants, including weight, density and cellularity coincide on (Q(X,R), ?UC). We find further conditions on X under which these cardinal invariants coincide on (Q(X,R), ?UC) as well as characterizations of some cardinal invariants of (Q(X,R), ?UC). It is known that the weight of continuous functions (C(R,R), ?UC) is ?0. We will show that the weight of (Q(R,R), ?UC) is 2c.


2018 ◽  
Vol 246 ◽  
pp. 137-143 ◽  
Author(s):  
Ľubica Holá ◽  
Dušan Holý

2017 ◽  
Vol 68 (1) ◽  
pp. 93-102
Author(s):  
L’ubica Holá ◽  
Dušan Holý

Abstract Let X be a locally compact space. A subfamily ℱ of the space D*(X, ℝ) of densely continuous forms with nonempty compact values from X to ℝ equipped with the topology 𝒯UC of uniform convergence on compact sets is compact if and only if {sup(F) : F ∈ ℱ} is compact in the space Q(X, ℝ) of quasicontinuous functions from X to ℝ equipped with the topology 𝒯UC.


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