Constructing the Banaschewski compactification through the functionally countable subalgebra of $C(X)$
| Autor: | Mehdi Parsinia |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
zero-dimensional space Mathematics::Operator Algebras Applied Mathematics lcsh:Mathematics Subalgebra Mathematics::General Topology banaschewski compactification Space (mathematics) Quotient space (linear algebra) lcsh:QA1-939 Combinatorics Computational Mathematics stone-$rm{check{c}}$ech compactification Discrete Mathematics and Combinatorics Countable set Compactification (mathematics) Analysis functionally countable subalgebra |
| Zdroj: | Categories and General Algebraic Structures with Applications, Vol 14, Iss 1, Pp 167-180 (2021) |
| ISSN: | 2345-5861 2345-5853 |
| Popis: | Let $X$ be a zero-dimensional space and $C_c(X)$ denote the functionally countable subalgebra of $C(X)$. It is well known that $\beta_0X$ (the Banaschewski compactfication of $X$) is a quotient space of $\beta X$. In this article, we investigate a construction of $\beta_0X$ via $\beta X$ by using $C_c(X)$ which determines the quotient space of $\beta X$ homeomorphic to $\beta_0X$. Moreover, the construction of $\upsilon_0X$ via $\upsilon_{_{C_c}}X$ (the subspace $\{p\in \beta X: \forall f\in C_c(X), f^*(p) |
| Databáze: | OpenAIRE |
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