Conditions for continuity of certain open monotone functions
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- by Melvin R. Hagan PDF
- Proc. Amer. Math. Soc. 30 (1971), 175-178 Request permission
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
- Melvin R. Hagan, A note on connected and peripherally continuous functions, Proc. Amer. Math. Soc. 26 (1970), 219–223. MR 263042, DOI 10.1090/S0002-9939-1970-0263042-6
- Paul E. Long, Properties of certain non-continuous transformations, Duke Math. J. 28 (1961), 639–645. MR 133111
- Paul E. Long, Connected mappings, Duke Math. J. 35 (1968), 677–682. MR 234428
- Gordon Thomas Whyburn, Analytic topology, American Mathematical Society Colloquium Publications, Vol. XXVIII, American Mathematical Society, Providence, R.I., 1963. MR 0182943
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 175-178
- MSC: Primary 54.60
- DOI: https://doi.org/10.1090/S0002-9939-1971-0279779-X
- MathSciNet review: 0279779