Geodesic
Lattice of subalgebras of the ring of continuous functions and Hewitt spaces
Matematičeskie zametki, Tome 62 (1997) no. 5, pp. 687-693.

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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. 
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     author = {E. M. Vechtomov},
     title = {Lattice of subalgebras of the ring of continuous functions and {Hewitt} spaces},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_5_a5/}
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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/

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