Continuity of certain connected functions and multifunctions
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- by Melvin R. Hagan PDF
- Proc. Amer. Math. Soc. 42 (1974), 295-301 Request permission
Abstract:
In this paper it is proved that if X is a 1st countable, locally connected, ${T_1}$-space and Y is a $\sigma$-coherent, sequentially compact ${T_1}$-space, then any nonmingled connectedness preserving multifunction from X onto Y with closed point values and connected inverse point values is upper semicontinuous. It follows that any monotone, connected, single-valued function from X onto Y is continuous. Let X be as above and let Y be a sequentially compact ${T_1}$-space with the property that if a descending sequence of connected sets has a nondegenerate intersection, then this intersection must contain at least three points. If f is a monotone connected single-valued function from X onto Y, then f is continuous. An example of a noncontinuous monotone connected function from a locally connected metric continuum onto an hereditarily locally connected metric continuum is given.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 295-301
- MSC: Primary 54C60
- DOI: https://doi.org/10.1090/S0002-9939-1974-0326652-7
- MathSciNet review: 0326652