THE ALPHA-BOUNDIFICATION OF ALPHA

dc.contributor.author	GarcíaFERREIRA, S
dc.contributor.author	Tamariz, A
dc.date.accessioned	2011-01-22T10:28:33Z
dc.date.available	2011-01-22T10:28:33Z
dc.date.issued	1993
dc.identifier.issn	0002-9939
dc.identifier.uri	http://hdl.handle.net/11154/3472
dc.description.abstract	A space X is < alpha-bounded if for all A subset-or-equal-to X with ]A] < alpha cl(x) A is compact. Let B (alpha) be the smallest < alpha-bounded subspace of beta (alpha) containing alpha. It is shown that the following properties are equivalent: (a) alpha is a singular cardinal	en_US
dc.description.abstract	(b) B(alpha) is not locally compact	en_US
dc.description.abstract	(c) B(alpha) is alpha-pseudocompact	en_US
dc.description.abstract	(d) B(alpha) is initially alpha-compact. Define B0(alpha) = alpha and B(n)(alpha) = {cl(beta)(alpha) A: A subset-or-equal-to (alpha), \A\ < alpha} for 0 < n < omega. We also prove that B2(alpha) not-equal B3(alpha) when omega = cf(alpha) < alpha. Finally, we calculate the cardinality of B(alpha) and prove that, for every singular cardinal alpha, \B(alpha)\ = \B(alpha)\alpha = \N(alpha)\cf(alpha) where N(alpha) = {p is-an-element-of beta(alpha): there is A is-an-element-of p with \A\ < alpha}.	en_US
dc.language.iso	en	en_US
dc.title	THE ALPHA-BOUNDIFICATION OF ALPHA	en_US
dc.type	Article	en_US
dc.identifier.idprometeo	3347
dc.source.novolpages	118(4):1301-1311
dc.subject.wos	Mathematics, Applied
dc.subject.wos	Mathematics
dc.description.index	WoS: SCI, SSCI o AHCI
dc.subject.keywords	LESS-THAN-ALPHA-BOUNDED SPACE
dc.subject.keywords	SINGULAR CARDINAL
dc.subject.keywords	REGULAR CARDINAL
dc.subject.keywords	ALPHA-GOOD POINT, WEAK P(ALPHA)-POINT
dc.subject.keywords	F-SPACE
dc.subject.keywords	ALPHA-PSEUDOCOMPACT
dc.subject.keywords	INITIALLY ALPHA-COMPACT
dc.relation.journal	Proceedings of the American Mathematical Society