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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Conditions for continuity of certain open monotone functions


Author: Melvin R. Hagan
Journal: Proc. Amer. Math. Soc. 30 (1971), 175-178
MSC: Primary 54.60
MathSciNet review: 0279779
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Abstract: In this paper continuity of certain open monotone functions is obtained by assuming for the domain and/or range various combinations of the properties of a metric continuum, regular metric continuum, semilocal connectedness, and hereditary local connectedness. An open monotone connected function from a hereditarily locally connected separable metric continuum onto a separable metric continuum is continuous. If the domain is a regular separable metric continuum, an upper semicontinuous decomposition and resulting monotone-light factorization yield continuity of an open monotone function with closed point inverses.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0279779-X
PII: S 0002-9939(1971)0279779-X
Keywords: Open monotone function, connected function, connectivity function, peripherally continuous function, regular continuum, semilocally connected, hereditarily locally connected, monotone-light factorization, upper semicontinuous decomposition
Article copyright: © Copyright 1971 American Mathematical Society