Concerning exactly images of continua

Authors:
Sam B. Nadler and L. E. Ward

Journal:
Proc. Amer. Math. Soc. **87** (1983), 351-354

MSC:
Primary 54F20; Secondary 54F50

DOI:
https://doi.org/10.1090/S0002-9939-1983-0681847-3

MathSciNet review:
681847

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Abstract | References | Similar Articles | Additional Information

Abstract: A surjective mapping is exactly if contains exactly points for each . We show that if is a continuum such that each nondegenerate subcontinuum of has an endpoint, and if , then there is no exactly mapping from any continuum onto . However, if is a continuum which contains a nonunicoherent subcontinuum, then such an mapping exists. Therefore, a Peano continuum is a dendrite if and only if for each there is no exactly mapping from any continuum onto . We also show that for each positive integer there is an exactly mapping from the Hilbert cube onto itself.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0681847-3

Keywords:
Exactly mapping,
continuum,
dendrite,
Hilbert cube

Article copyright:
© Copyright 1983
American Mathematical Society