Remainders of metrizable and close to metrizable spaces

• Autorzy: A. V. Arhangel'skii
• Języki publikacji: EN

Abstrakty

EN

We continue the study of remainders of metrizable spaces, expanding and applying results obtained in [Fund. Math. 215 (2011)]. Some new facts are established. In particular, the closure of any countable subset in the remainder of a metrizable space is a Lindelöf p-space. Hence, if a remainder of a metrizable space is separable, then this remainder is a Lindelöf p-space. If the density of a remainder Y of a metrizable space does not exceed $2^{ω}$, then Y is a Lindelöf Σ-space. We also show that many of the theorems on remainders of metrizable spaces can be extended to paracompact p-spaces or to spaces with a σ-disjoint base. We also extend to remainders of metrizable spaces the well known theorem on metrizability of compacta with a point-countable base.

Kategorie tematyczne

• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54B05: Subspaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 220
• Numer: 1
• Strony: 71-81

Daty

wydano

2013

Twórcy

autor

A. V. Arhangel'skii

• h. 33, apt. 137 Kutuzovskii Prospekt, Moscow 121165, Russian Federation

Identyfikatory

DOI

10.4064/fm220-1-4