|Conţinutul numărului revistei|
| SM ISO690:2012|
ARHANGELISKI, Alexandr, CHOBAN, Mitrofan. Properties of remainders of topological groups and of their perfect images. In: Topology and its Applications, 2021, nr. 296, p. 0. ISSN 0166-8641. DOI: 10.1016/j.topol.2021.107687
|Topology and its Applications|
|Numărul 296 / 2021 / ISSN 0166-8641|
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 Gδ-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).
Group extension, Group remainder, Metacompact, paracompact p-space, Perfect mapping, Point-finitely complete, Rajkov remainder, Topological group