A characterization of complete metric spaces

Author:
Francis Sullivan

Journal:
Proc. Amer. Math. Soc. **83** (1981), 345-346

MSC:
Primary 54E50; Secondary 54C30

MathSciNet review:
624927

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A general formulation of the completeness argument used in the Bishop-Phelps Theorem and many other places has been given by Ekeland. It is shown that Ekeland's formulation characterizes complete metric spaces.

**[1]**H. Brézis and F. E. Browder,*A general principle on ordered sets in nonlinear functional analysis*, Advances in Math.**21**(1976), no. 3, 355–364. MR**0425688****[2]**James Caristi,*Fixed point theorems for mappings satisfying inwardness conditions*, Trans. Amer. Math. Soc.**215**(1976), 241–251. MR**0394329**, 10.1090/S0002-9947-1976-0394329-4**[3]**I. Ekeland,*On the variational principle*, J. Math. Anal. Appl.**47**(1974), 324–353. MR**0346619****[4]**Ivar Ekeland,*Nonconvex minimization problems*, Bull. Amer. Math. Soc. (N.S.)**1**(1979), no. 3, 443–474. MR**526967**, 10.1090/S0273-0979-1979-14595-6**[5]**W. A. Kirk,*Caristi’s fixed point theorem and the theory of normal solvability*, Fixed point theory and its applications (Proc. Sem., Dalhousie Univ., Halifax, N.S., 1975) Academic Press, New York, 1976, pp. 109–120. MR**0454754****[6]**W. A. Kirk,*Caristi’s fixed point theorem and metric convexity*, Colloq. Math.**36**(1976), no. 1, 81–86. MR**0436111****[7]**R. R. Phelps,*Support cones in Banach spaces and their applications*, Advances in Math.**13**(1974), 1–19. MR**0338741**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
54E50,
54C30

Retrieve articles in all journals with MSC: 54E50, 54C30

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1981-0624927-9

Keywords:
Bishop-Phelps Theorem,
completeness

Article copyright:
© Copyright 1981
American Mathematical Society