Given a compactification aX of a Tichonoff space X, let f_a be the canonical quotient map from the Stone-Čech compactification bX of X onto aX. It is known that the complete upper semi-lattice K(X) of all compactifications of X is a lattice whenever the set F(aX) of nontrivial fibers of f_a is finite for all compactifications aX of X. We give some necessary and sufficient conditions, in terms of X and bX-X, for F(aX) to be finite for all aX in K(X).
Special lattices of compactifications
CATERINO, Alessandro
1985
Abstract
Given a compactification aX of a Tichonoff space X, let f_a be the canonical quotient map from the Stone-Čech compactification bX of X onto aX. It is known that the complete upper semi-lattice K(X) of all compactifications of X is a lattice whenever the set F(aX) of nontrivial fibers of f_a is finite for all compactifications aX of X. We give some necessary and sufficient conditions, in terms of X and bX-X, for F(aX) to be finite for all aX in K(X).File in questo prodotto:
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