Open AccessCovering properties of Cp(X) and Ck(X)
Author(s) -
J. C. Ferrando,
Manuel López Pellicer
Publication year - 2020
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/fil2011575f
Subject(s) - mathematics , cardinality (data modeling) , tychonoff space , pointwise , bounded function , countable set , closure (psychology) , space (punctuation) , locally compact space , compact space , discrete mathematics , combinatorics , topology (electrical circuits) , pure mathematics , topological space , mathematical analysis , data mining , linguistics , philosophy , computer science , economics , market economy
Let X be a Tychonoff space. We survey some classic and recent results that characterize the topology or cardinality of X when Cp (X) or Ck (X) is covered by certain families of sets (sequences, resolutions, closure-preserving coverings, compact coverings ordered by a second countable space) which swallow or not some classes of sets (compact sets, functionally bounded sets, pointwise bounded sets) in C(X).