Open AccessQuasicontinuous functions and the topology of uniform convergence on compacta
Author(s) -
Ľubica Holá,
Dušan Holý
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2103911h
Subject(s) - mathematics , metrization theorem , hausdorff space , topology (electrical circuits) , topological space , uniform convergence , space (punctuation) , convergence (economics) , pure mathematics , discrete mathematics , combinatorics , mathematical analysis , separable space , computer network , linguistics , philosophy , bandwidth (computing) , computer science , economics , economic growth
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.