Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] M. R. Hagan, A note on connected and peripherally continuous functions. Proc. Amer. Math. Soc. 26 (1970), 219-223. MR 0263042 (41:7647)
  • [2] P. E. Long, Properties of certain non-continuous transformations, Duke Math. J. 28 (1961), 639-645. MR 24 #A2945. MR 0133111 (24:A2945)
  • [3] -, Connected mappings, Duke Math. J. 35 (1968), 677-682. MR 38 #2745. MR 0234428 (38:2745)
  • [4] G. T. Whyburn, Analytic topology, Amer. Math. Soc. Colloq. Publ., vol. 28, Amer. Math. Soc., Providence, R. I., 1963. MR 32 #425. MR 0182943 (32:425)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.60

Retrieve articles in all journals with MSC: 54.60

Additional Information

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

American Mathematical Society