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

• Autorzy: Jesús M. Domínguez
• Języki publikacji: 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.

Kategorie tematyczne

• 54C40: Algebraic properties of function spaces
• 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 178
• Numer: 3
• Strony: 203-215

Daty

wydano

2003

Twórcy

autor

Jesús M. Domínguez

• Departamento de Álgebra, Geometría y Topología, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid, Spain

Identyfikatory

DOI

10.4064/fm178-3-2