Countable tightness and $${\mathfrak {G}}$$-bases on free topological groups
| Autor: | Jing Zhang, Alex Ravsky, Fucai Lin |
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| Rok vydání: | 2020 |
| Předmět: |
Algebra and Number Theory
54H11 22A05 (Primary) 54E20 54E35 54D50 54D55 (Secondary) Markov chain Applied Mathematics Tychonoff space 010102 general mathematics General Topology (math.GN) Mathematics::General Topology Group Theory (math.GR) 01 natural sciences 010101 applied mathematics Combinatorics Computational Mathematics FOS: Mathematics Countable set Geometry and Topology Topological group 0101 mathematics Abelian group Mathematics - Group Theory Analysis Mathematics - General Topology Mathematics |
| Zdroj: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 114 |
| ISSN: | 1579-1505 1578-7303 |
| Popis: | Given a Tychonoff space $X$, let $F(X)$ and $A(X)$ be respectively the free topological group and the free Abelian topological group over $X$ in the sense of Markov. In this paper, we consider two topological properties of $F(X)$ or $A(X)$, namely the countable tightness and $\mathfrak G$-base. We provide some characterizations of the countable tightness and $\mathfrak G$-base of $F(X)$ and $A(X)$ for various special classes of spaces $X$. Furthermore, we also study the countable tightness and $\mathfrak G$-base of some $F_{n}(X)$ of $F(X)$. Comment: 11 |
| Databáze: | OpenAIRE |
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