Displaying similar documents to “κ-compactness, extent and the Lindelöf number in LOTS”

Between closed sets and generalized closed sets in closure spaces

Chawalit Boonpok, Jeeranunt Khampakdee (2008)

Acta Mathematica Universitatis Ostraviensis

Similarity:

The purpose of the present paper is to define and study ∂ -closed sets in closure spaces obtained as generalization of the usual closed sets. We introduce the concepts of ∂ -continuous and ∂ -closed maps by using ∂ -closed sets and investigate some of their properties.

The sup = max problem for the extent of generalized metric spaces

Yasushi Hirata, Yukinobu Yajima (2013)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

It looks not useful to study the sup = max problem for extent, because there are simple examples refuting the condition. On the other hand, the sup = max problem for Lindelöf degree does not occur at a glance, because Lindelöf degree is usually defined by not supremum but minimum. Nevertheless, in this paper, we discuss the sup = max problem for the extent of generalized metric spaces by combining the sup = max problem for the Lindelöf degree of these spaces.

Property ( a ) and dominating families

Samuel Gomes da Silva (2005)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Generalizations of earlier negative results on Property ( a ) are proved and two questions on an ( a ) -version of Jones’ Lemma are posed. We discuss these questions in the realm of locally compact spaces. Using dominating families of functions as a tool, we prove that under the assumptions “ 2 ω is regular” and “ 2 ω < 2 ω 1 ” the existence of a T 1 separable locally compact ( a ) -space with an uncountable closed discrete subset implies the existence of inner models with measurable cardinals. We also use cardinal...