A characterization of metric completeness

Author:
J. D. Weston

Journal:
Proc. Amer. Math. Soc. **64** (1977), 186-188

MSC:
Primary 54C30

MathSciNet review:
0458359

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Abstract | References | Similar Articles | Additional Information

Abstract: A proof is given of a theorem, relevant to fixed-point theory, which implies that a metric space (*X, d*) is complete if and only if, for each continuous function bounded below on *X*, there is a point such that for every other point *x*.

**[1]**Chi Song Wong,*On a fixed point theorem of contractive type*, Proc. Amer. Math. Soc.**57**(1976), no. 2, 283–284. MR**0407826**, 10.1090/S0002-9939-1976-0407826-5**[2]**B. Fisher,*A fixed point theorem*, Math. Mag.**48**(1975), no. 4, 223–225. MR**0377842**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0458359-2

Keywords:
Completeness,
fixed point,
metric space,
order,
semicontinuity

Article copyright:
© Copyright 1977
American Mathematical Society