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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Continuously extending partial functions

Author(s): Phillip Zenor
Journal: Proc. Amer. Math. Soc. 135 (2007), 305-312.
MSC (2000): Primary 54D15, 54C20, 54C30
Posted: June 13, 2006
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Abstract: We characterize those Hausdorff spaces in which continuous functions defined on compact subsets can be continuously extended to continuous functions defined on the space.


References:

1.
A. V. Arhangel'ski{\u{\i\/}}\kern.15em, On a class of spaces containing all metric and all locally bicompact spaces (Russian) Dokl. Akad. Nauk SSSR 151 (1963), 751-754. MR 0152988 (27:2959)

2.
Harold R. Bennett and David J. Lutzer, Continuous separating families in ordered spaces and strong base conditions, Topology Appl. 119 (2002), no. 3, 305-314. MR 1888675 (2002m:54034)

3.
Lorenz Halbeisen and Norbert Hungerbühler, On continuously Urysohn and strongly separating spaces, Topology Appl. 118 (2002), no. 3, 329-335. MR 1874554 (2002j:54041)

4.
H. P. Künzi and L. B. Shapiro, On simultaneous extension of continuous partial functions, Proc. Amer. Math. Soc. 125 (1997), 1853-1859. MR 1415348 (98g:54015)

5.
K. Kuratowski, Sur l'espace des fonctions partielles, Ann. Mat. Pura Appl. 40 (1955), 61-67. MR 0074807 (17:650b)

6.
K. Kuratowski, Sur une méthode de métrisation complète de certains espaces d'ensembles compacts, Fund. Math. 43 (1956), 114-138. MR 0079258 (18:58a)

7.
E. N. Stepanova, Continuation of continuous functions and the metrizability of paracompact p-spaces (Russian), Mat. Zamitki 53 (1993), no. 3, 92-101; translation in Math. Notes 53 (1993), no. 3-4, 308-314. MR 1220188 (94k:54031)

8.
P. L. Zenor, Extending continuous functions in compact metric spaces, Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg, Va., 1973), pp. 277-283. Lecture Notes in Math., Vol. 375, Springer, Berlin, 1974. MR 0355950 (50:8423)


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Additional Information:

Phillip Zenor
Affiliation: Department of Mathematics, Auburn University, Alabama 36849

DOI: 10.1090/S0002-9939-06-08432-2
PII: S 0002-9939(06)08432-2
Received by editor(s): January 1, 2004
Received by editor(s) in revised form: July 15, 2005
Posted: June 13, 2006
Communicated by: Alan Dow
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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