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The structure of Valdivia compact lines
- 1.0342854 - MÚ 2011 RIV NL eng J - Journal Article
Kalenda, O.F.K. - Kubiś, Wieslaw
The structure of Valdivia compact lines.
Topology and its Applications. Roč. 157, č. 7 (2010), s. 1142-1151. ISSN 0166-8641. E-ISSN 1879-3207
R&D Projects: GA AV ČR IAA100190901
Institutional research plan: CEZ:AV0Z10190503
Keywords : valdivia compact line * increasing map * retraction
Subject RIV: BA - General Mathematics
Impact factor: 0.447, year: 2010
http://www.sciencedirect.com/science/article/pii/S0166864110000374
We study linearly ordered spaces which are Valdivia compact in their order topology. We find an internal characterization of these spaces and we present a counter-example disproving a conjecture posed earlier by the first author. The conjecture asserted that a compact line is Valdivia compact if its weight does not exceed 8(1), every point of uncountable character is isolated from one side and every closed first countable subspace is metrizable. It turns out that the last condition is not sufficient. On the other hand, we show that the conjecture is valid if the closure of the set of points of uncountable character is scattered. This improves an earlier result of the first author.
Permanent Link: http://hdl.handle.net/11104/0185473
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Number of the records: 1