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A short proof that hyperspaces of Peano continua are absolute retracts
Author(s):
Sergey
Antonyan
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2187-2189.
MSC (2000):
Primary 54B20;
Secondary 54C55
Posted:
February 15, 2001
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Abstract:
We give a short proof of Wojdyslawski's famous theorem.
References:
- 1.
- D. W. Curtis, Hyperspaces of noncompact metric spaces, Compositio Math. 40 (1980), 139-152. MR 81c:54009
- 2.
- K. Borsuk, Theory of retracts, PWN-Polish Scientific Publishers, Warsaw, 1967. MR 35:7306
- 3.
- J. Dugundji, An extension of Tietze's theorem, Pac. J. Math. 1 (1951), 353-367. MR 13:373c
- 4.
- J. Kelley, Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22-36. MR 3:315b
- 5.
- J. van Mill, Infinite-dimensional topology. Prerequisites and Introduction, North Holland, 1989. MR 90a:57025
- 6.
- M. Wojdyslawski, Retracts absolutes et hyperespaces des continus, Fund. Math. 32 (1939), 184-192.
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Additional Information:
Sergey
Antonyan
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, UNAM, Circuito Exterior, C.U., 04510, México D.F., México
Email:
antonyan@servidor.unam.mx
DOI:
10.1090/S0002-9939-01-06098-1
PII:
S 0002-9939(01)06098-1
Keywords:
Peano continuum,
absolute retract,
hyperspace,
canonical cover,
nerve
Received by editor(s):
October 29, 1999
Received by editor(s) in revised form:
September 5, 2000
Posted:
February 15, 2001
Additional Notes:
The author was partially supported by PAPIIT (UNAM) research grant IN105800
Communicated by:
Alan Dow
Copyright of article:
Copyright
2001,
American Mathematical Society
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