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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2003 | 178 | 3 | 203-215

## A generating family for the Freudenthal compactification of a class of rimcompact spaces

EN

### Abstrakty

EN
For X a Tikhonov space, let F(X) be the algebra of all real-valued continuous functions on X that assume only finitely many values outside some compact subset. We show that F(X) generates a compactification γX of X if and only if X has a base of open sets whose boundaries have compact neighborhoods, and we note that if this happens then γX is the Freudenthal compactification of X. For X Hausdorff and locally compact, we establish an isomorphism between the lattice of all subalgebras of $F(X)/C_{K}(X)$ and the lattice of all compactifications of X with zero-dimensional remainder, the finite-dimensional subalgebras corresponding to the compactifications with finite remainder.

203-215

wydano
2003

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