Properties of remainders of topological groups and of their perfect images

Arhangeliski Alexandr; Choban Mitrofan

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SM ISO690:2012

ARHANGELISKI, Alexandr, CHOBAN, Mitrofan. Properties of remainders of topological groups and of their perfect images. In: Topology and its Applications, 2021, vol. 296, p. 0. ISSN 0166-8641. DOI: https://doi.org/10.1016/j.topol.2021.107687

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Topology and its Applications

Volumul 296 / 2021 / ISSN 0166-8641

Properties of remainders of topological groups and of their perfect images

DOI:https://doi.org/10.1016/j.topol.2021.107687

Pag. 0-0

Arhangeliski Alexandr¹, Choban Mitrofan²

¹ Moscow State Pedagogical University,
² Tiraspol State University

Disponibil în IBN: 29 aprilie 2021

Rezumat

If X is a dense subspace of a space B, then B is called an extension of X, and the subspace Y = B∖X is called a remainder of X. We study below, how the properties of remainders of spaces influence the properties of these spaces. In particular, we establish the following fact: if Y is a remainder of a topological group G in an extension B of G, and every closed pseudocompact G_δ-subspace of Y is compact, and B contains a nonempty compact subset Φ of countable character in B such that G∩Φ≠∅, then G is a paracompact p-space (Theorem 2.3). This fact plays a key role in the proofs of the similar statements for images and preimages of topological groups under perfect mappings (see Theorems 3.1, 3.2 and 3.4).

Cuvinte-cheie
Group extension, Group remainder, Metacompact, paracompact p-space, Perfect mapping, Point-finitely complete, Rajkov remainder, Topological group

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<dc:creator>Arhangeliski, A.V.</dc:creator>
<dc:creator>Cioban, M.M.</dc:creator>
<dc:date>2021-06-01</dc:date>
<dc:description xml:lang='en'><p>If X is a dense subspace of a space B, then B is called an extension of X, and the subspace Y = B∖X is called a remainder of X. We study below, how the properties of remainders of spaces influence the properties of these spaces. In particular, we establish the following fact: if Y is a remainder of a topological group G in an extension B of G, and every closed pseudocompact G<sub>&delta;</sub>-subspace of Y is compact, and B contains a nonempty compact subset &Phi; of countable character in B such that G&cap;&Phi;&ne;&empty;, then G is a paracompact p-space (Theorem 2.3). This fact plays a key role in the proofs of the similar statements for images and preimages of topological groups under perfect mappings (see Theorems 3.1, 3.2 and 3.4).&nbsp;</p></dc:description>
<dc:identifier>10.1016/j.topol.2021.107687</dc:identifier>
<dc:source>Topology and its Applications  () 0-0</dc:source>
<dc:subject>Group extension</dc:subject>
<dc:subject>Group remainder</dc:subject>
<dc:subject>Metacompact</dc:subject>
<dc:subject>paracompact p-space</dc:subject>
<dc:subject>Perfect mapping</dc:subject>
<dc:subject>Point-finitely complete</dc:subject>
<dc:subject>Rajkov remainder</dc:subject>
<dc:subject>Topological group</dc:subject>
<dc:title>Properties of remainders of topological groups and of their perfect images</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
</oai_dc:dc>