Lattice of subalgebras of the ring of continuous functions and Hewitt spaces
Matematičeskie zametki, Tome 62 (1997) no. 5, pp. 687-693
Voir la notice de l'article provenant de la source Math-Net.Ru
The lattice $A(X)$ of all possible subalgebras of the ring of all continuous $\mathbb R$-valued functions defined on an $\mathbb R$-separated space $X$ is considered. A topological space is said to be a Hewitt space if it is homeomorphic to a closed subspace of a Tychonoff power of the real line $\mathbb R$. The main achievement of the paper is the proof of the fact that any Hewitt space $X$ is determined by the lattice $A(X)$. An original technique of minimal and maximal subalgebras is applied. It is shown that the lattice $A(X)$ is regular if and only if $X$ contains at most two points.
@article{MZM_1997_62_5_a5,
author = {E. M. Vechtomov},
title = {Lattice of subalgebras of the ring of continuous functions and {Hewitt} spaces},
journal = {Matemati\v{c}eskie zametki},
pages = {687--693},
publisher = {mathdoc},
volume = {62},
number = {5},
year = {1997},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_5_a5/}
}
E. M. Vechtomov. Lattice of subalgebras of the ring of continuous functions and Hewitt spaces. Matematičeskie zametki, Tome 62 (1997) no. 5, pp. 687-693. http://geodesic.mathdoc.fr/item/MZM_1997_62_5_a5/