Real Analysis Exchange

An Almost Continuous Nonextendable Function

Harvey Rosen

Full-text: Open access

Abstract

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 in \cite{R11}. Results about stationary sets are given for the class of extendable functions from \(I\) into \(I\), where \(I = [0,1]\).

Article information

Source
Real Anal. Exchange, Volume 23, Number 2 (1999), 567-570.

Dates
First available in Project Euclid: 14 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1337001366

Mathematical Reviews number (MathSciNet)
MR1639980

Zentralblatt MATH identifier
0943.26009

Subjects
Primary: 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 54C08: Weak and generalized continuity

Keywords
{almost continuous function} {extendable connectivity function} {the Strong Cantor Intermediate Value Property} {stationary set}

Citation

Rosen, Harvey. An Almost Continuous Nonextendable Function. Real Anal. Exchange 23 (1999), no. 2, 567--570. https://projecteuclid.org/euclid.rae/1337001366


Export citation