Document Zbl 0943.26009

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An almost continuous nonextendable function. (English) Zbl 0943.26009

Real Anal. Exch. 23(1997-98), No. 2, 567-570 (1998).

Summary: An example is constructed under the Continuum Hypothesis showing that almost continuity and the Strong Cantor Intermediate Value Property do not imply extendability. This answers a question of H. Rosen, R. G. Gibson and F. Roush [Real Anal. Exch. 17, No. 1, 248-257 (1992; Zbl 0747.26008)]. Results about stationary sets are given for the class of extendable functions from \(I\) into \(I\), where \(I = [0,1]\).

MSC:

26A15	Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
54C08	Weak and generalized continuity

Keywords:

almost continuous function; extendable connectivity function; the Strong Cantor Intermediate Value Property; stationary set

Citations:

Zbl 0747.26008

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