# The minimum uniform compactification of a metric space

Fundamenta Mathematicae (1995)

- Volume: 147, Issue: 1, page 39-59
- ISSN: 0016-2736

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topGrant Woods, R.. "The minimum uniform compactification of a metric space." Fundamenta Mathematicae 147.1 (1995): 39-59. <http://eudml.org/doc/212073>.

@article{GrantWoods1995,

abstract = {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.},

author = {Grant Woods, R.},

journal = {Fundamenta Mathematicae},

keywords = {proximity; remainder; Smirnov compactification},

language = {eng},

number = {1},

pages = {39-59},

title = {The minimum uniform compactification of a metric space},

url = {http://eudml.org/doc/212073},

volume = {147},

year = {1995},

}

TY - JOUR

AU - Grant Woods, R.

TI - The minimum uniform compactification of a metric space

JO - Fundamenta Mathematicae

PY - 1995

VL - 147

IS - 1

SP - 39

EP - 59

AB - 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.

LA - eng

KW - proximity; remainder; Smirnov compactification

UR - http://eudml.org/doc/212073

ER -

## References

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