Darboux retracts

Darboux retracts are defined, and it is proved that any continuum contained in a separable metric space is a Darboux retract. This leads immediately to a very general extension theorem.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1980-07, Vol.79 (3), p.491-494
Main Authors: Roush, Fred, Gibson, Richard G., Kellum, Kenneth R.
Format: Article
Language:English
Subjects:
Connectivity
Cornettes
Mathematical functions
Mathematical theorems
Mathematics
Numbers
Real numbers
Separable spaces
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Description
Summary:Darboux retracts are defined, and it is proved that any continuum contained in a separable metric space is a Darboux retract. This leads immediately to a very general extension theorem.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-1980-0568000-6