The minimum uniform compactification of a metric space

• Autorzy: R. Grant Woods
• Języki publikacji: EN

Abstrakty

EN

It is shown that associated with each metric space (X,d) there is a compactification $u_dX$ of X that can be characterized as the smallest compactification of X to which each bounded uniformly continuous real-valued continuous function with domain X can be extended. Other characterizations of $u_dX$ are presented, and a detailed study of the structure of $u_dX$ is undertaken. This culminates in a topological characterization of the outgrowth $u_dℝ^n ∖ ℝ^n$, where $(ℝ^n,d)$ is Euclidean n-space with its usual metric.

Kategorie tematyczne

• 54E35: Metric spaces, metrizability
• 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1995
• Tom: 147
• Numer: 1
• Strony: 39-59

Daty

wydano

1995

otrzymano

1994-02-15

poprawiono

1994-08-31

poprawiono

1994-12-02

Twórcy

autor

R. Grant Woods

• Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2

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