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Remainders of metrizable and close to metrizable spaces. (English) Zbl 1267.54024
The paper deals with remainders $$Y$$ of a Tychonoff space $$X$$ which are Lindelöf $$\Sigma$$-spaces or Lindelöf $$p$$-spaces. We mention a few typical results. If $$X$$ is a Tychonoff space having a $$\sigma$$-disjoint base $$\mathcal B$$ of cardinality $$\leq 2^{\omega}$$, then every remainder of $$X$$ is a Lindelöf $$\Sigma$$-space. For Lindelöf spaces this assertion is true without cardinal restrictions on $$\mathcal B$$. Let $$X$$ be a paracompact $$p$$-space. Then every remainder $$Y$$ of $$X$$ satisfies: (1) for any $$A\subset Y$$ of cardinality $$\leq 2^{\omega}$$ the closure of $$A$$ in $$Y$$ is a Lindelöf $$\Sigma$$-space, (2) any closed $$P\subset Y$$ with the ccc property is a Lindelöf $$p$$-space, (3) If $$X$$ has a separable remainder, then $$Y$$ is a Lindelöf $$p$$-space.

##### MSC:
 54D40 Remainders in general topology 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 54B05 Subspaces in general topology 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 54E35 Metric spaces, metrizability
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