The Degree of Weakly Discretely Generated Spaces

作者：Alas O T; Junqueira L R^*; Wilson R G

来源：Acta Mathematica Hungarica, 2014, 143(2): 453-465.

DOI：10.1007/s10474-014-0417-1

• discretely generated space
• weakly discretely generated space
• one point compactification
• Stone-Cech compactification
• Katetov extension
• ordinal function idc

A space X is discretely generated at a point if for any with , there exists a discrete set such that . The space X is discretely generated if it is discretely generated at every point . We say that X is weakly discretely generated if for any non-closed set , there exists a discrete set such that . New results about these properties in the classes of pseudocompact and ech-complete spaces are obtained and a theorem of Ivanov and Osipov concerning the ordinal function idc is generalized to the class of ech-complete spaces.

• 出版日期2014-8