Recently, in Cammaroto et al. (2013) [4] we obtained a generalization of the famous inequality established by A.V. Arhangelʼskiĭ in 1969 for Hausdoff spaces. In this paper, following this line of research, we present a common variation of this inequality for Urysohn spaces by developing a Main Theorem for obtaining inequalities. In particular, we extend a 2006 inequality by Hodel for Urysohn spaces. Moreover, this extended inequality is used to analyze a result containing an increasing chain of spaces that satisfies the same cardinality inequality and this new result solves an open problem in Cammaroto et al. (2013) [4] for Urysohn spaces. This general theorem also provides a new cardinal inequality for Hausdorff spaces. The paper is concluded with some open problems.
On the cardinality of Urysohn spaces
CAMMAROTO, Filippo;CATALIOTO, ANDREI;
2013-01-01
Abstract
Recently, in Cammaroto et al. (2013) [4] we obtained a generalization of the famous inequality established by A.V. Arhangelʼskiĭ in 1969 for Hausdoff spaces. In this paper, following this line of research, we present a common variation of this inequality for Urysohn spaces by developing a Main Theorem for obtaining inequalities. In particular, we extend a 2006 inequality by Hodel for Urysohn spaces. Moreover, this extended inequality is used to analyze a result containing an increasing chain of spaces that satisfies the same cardinality inequality and this new result solves an open problem in Cammaroto et al. (2013) [4] for Urysohn spaces. This general theorem also provides a new cardinal inequality for Hausdorff spaces. The paper is concluded with some open problems.Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
