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Two examples concerning almost continuous functions

Krzysztof Ciesielski·Andrzej Roslanowski
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Abstract

We construct, under the assumption that union of less than continuum many meager subsets of R is meager in R, an additive connectivity function f:R-->R with Cantor intermediate value property which is not almost continuous. This gives a partial answer to a question of D. Banaszewski. We also show that every extendable function g:R-->R with a dense graph satisfies the following stronger version of the SCIVP property: for every a R which has the strong Cantor intermediate value property but is not extendable. This answers a question of H. Rosen. This also generalizes Rosen's result that a similar (but not additive) function exists under the assumption of the continuum hypothesis.

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BibTeXRIS

Krzysztof Ciesielski, Andrzej Roslanowski. 1998-11-03. Two examples concerning almost continuous functions. https://arxiv.org/abs/math/9811011

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