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Z-pseudocompact

Last-modified: 2010-07-23 (金) 14:48:50

Definition Edit

Let C(X,Z) denote the ring of all integer-valued continuous functions on a topological spaces and C^*(X,Z) the ring of all bounded integer-valued continuous functions.
X is called Z-pseudocompact if C(X,Z)=C^*(X,Z).

Reference Edit

R. S. Pierce, Rings of Integer-Valued Continuous Functions, Transactions of the American Mathematical Society, Vol.100, No.3(1961), pp.371-394.