Quantcast
Channel: User Elliot Glazer - MathOverflow
Viewing all articles
Browse latest Browse all 76

Comment by Elliot Glazer on Sequential continuity and the Axiom of Choice

$
0
0
Yes, that fails for the indicator function of an infinite Dedekind finite set $S:$ globally sequentially usco, sequentially continuous off $S,$ discontinuous at the condensation points of $S$ (which is a perfect set so is not contained in $S$). If you demanded $f$ be in some Baire class AND usco, it would be significantly harder to find a counterexample.

Viewing all articles
Browse latest Browse all 76