Georgian Mathematical Journal
Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.
Editorial Board Member: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio
4 Issues per year
IMPACT FACTOR 2016: 0.290
5-year IMPACT FACTOR: 0.430
CiteScore 2016: 0.46
SCImago Journal Rank (SJR) 2015: 0.355
Source Normalized Impact per Paper (SNIP) 2015: 0.939
Mathematical Citation Quotient (MCQ) 2015: 0.25
On precompact sets in spaces Cc(X)
We show that the fact that X has a compact resolution swallowing the compact sets characterizes those Cc(X) spaces which have the so-called 𝔊-base. So, if X has a compact resolution which swallows all compact sets, then Cc(X) belongs to the class 𝔊 of Cascales and Orihuela (a large class of locally convex spaces which includes the (LM) and (DF)-spaces) for which all precompact sets are metrizable and, conversely, if Cc(X) belongs to the class 𝔊 and X satisfies an additional mild condition, then X has a compact resolution which swallows all compact sets. This fully applicable result extends the classification of locally convex properties (due to Nachbin, Shirota, Warner and others) of the space Cc(X) in terms of topological properties of X and leads to a nice theorem of Cascales and Orihuela stating that for X containing a dense subspace with a compact resolution, every compact set in Cc(X) is metrizable.
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.