Remainders of metrizable spaces and a generalization of Lindelöf Σ-spaces

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

Abstrakty

EN

We establish some new properties of remainders of metrizable spaces. In particular, we show that if the weight of a metrizable space X does not exceed $2^{ω}$, then any remainder of X in a Hausdorff compactification is a Lindelöf Σ-space. An example of a metrizable space whose remainder in some compactification is not a Lindelöf Σ-space is given. A new class of topological spaces naturally extending the class of Lindelöf Σ-spaces is introduced and studied. This leads to the following theorem: if a metrizable space X has a remainder Y with a $G_{δ}$-diagonal, then both X and Y are separable and metrizable. Some new results on remainders of topological groups are also established.

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: 2011
• Tom: 215
• Numer: 1
• Strony: 87-100

Daty

wydano

2011

Twórcy

autor

A. V. Arhangel'skii

• Moscow 121165, Russia

Identyfikatory

DOI

10.4064/fm215-1-5