Continuity of monotone functions

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Apr 1982 English Publisher:Mathematical Sciences PublishersJournal:Pacific Journal of Mathematics, volume 99, pages 413-418 (issn: 0030-8730, eissn: 0030-8730,

Copyright policy )

Authors: Mandelkern, Mark;

doi: 10.2140/pjm.1982.99.413

Continuity of monotone functions

- Summary
- Subjects
- Metrics

Abstract

The author has obtained the following results for real functions on the closed unit interval in the style of \textit{E. A. Bishop's} ''Foundations of constructive analysis'' (1967): (Theorem 1) For nondecreasing f the following are equivalent, pointwise continuity, uniform continuity, f is antidecreasing \((f(x)

Keywords

26A48, monotone functions, 03F65, Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable, intermediate values, pointwise continuity, Other constructive mathematics, constructive analysis, Monotonic functions, generalizations, uniform continuity

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	12
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average