New classes of compact-type spaces
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914112305364992 |
|---|---|
| author | Gabriyelyan, Saak Reznichenko, Evgenii |
| author_facet | Gabriyelyan, Saak Reznichenko, Evgenii |
| contents | Being motivated by the notions of $κ$-Fréchet--Urysohn spaces and $k'$-spaces introduced by Arhangel'skii, the notion of sequential spaces and the study of Ascoli spaces, we introduce three new classes of compact-type spaces. They are defined by the possibility to attain each or some of boundary points $x$ of an open set $U$ by a sequence in $U$ converging to $x$ or by a relatively compact subset $A\subseteq U$ such that $x\in \overline{A}$. Relationships of the introduced classes with the classical classes (as, for example, the classes of $κ$-Fréchet--Urysohn spaces, (sequentially) Ascoli spaces, $k_{\mathbb R}$-spaces, $s_{\mathbb R}$-spaces etc.) are given. We characterize these new classes of spaces and study them with respect to taking products, subspaces and quotients. In particular, we give new characterizations of $κ$-Fréchet--Urysohn spaces and show that each feathered topological group is $κ$-Fréchet--Urysohn. We describe locally compact abelian groups which endowed with the Bohr topology belong to one of the aforementioned classes. Numerous examples are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New classes of compact-type spaces Gabriyelyan, Saak Reznichenko, Evgenii General Topology Functional Analysis 54A20 54C10 54D50 54D55 Being motivated by the notions of $κ$-Fréchet--Urysohn spaces and $k'$-spaces introduced by Arhangel'skii, the notion of sequential spaces and the study of Ascoli spaces, we introduce three new classes of compact-type spaces. They are defined by the possibility to attain each or some of boundary points $x$ of an open set $U$ by a sequence in $U$ converging to $x$ or by a relatively compact subset $A\subseteq U$ such that $x\in \overline{A}$. Relationships of the introduced classes with the classical classes (as, for example, the classes of $κ$-Fréchet--Urysohn spaces, (sequentially) Ascoli spaces, $k_{\mathbb R}$-spaces, $s_{\mathbb R}$-spaces etc.) are given. We characterize these new classes of spaces and study them with respect to taking products, subspaces and quotients. In particular, we give new characterizations of $κ$-Fréchet--Urysohn spaces and show that each feathered topological group is $κ$-Fréchet--Urysohn. We describe locally compact abelian groups which endowed with the Bohr topology belong to one of the aforementioned classes. Numerous examples are given. |
| title | New classes of compact-type spaces |
| topic | General Topology Functional Analysis 54A20 54C10 54D50 54D55 |
| url | https://arxiv.org/abs/2510.21642 |