The structure of Valdivia compact lines

0342854 - MÚ 2011 RIV NL eng J - Článek v odborném periodiku
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
Grant CEP: GA AV ČR IAA100190901
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: valdivia compact line * increasing map * retraction
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.447, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0185473