Some results on separate and joint continuity

Details Some results on separate and joint continuity Some results on separate and joint continuity

2009-09-11

arxiv.org/abs/0909.2231v1

Topology and its Applications, Volume 157, Issue 2, 1 February 2010, Pages 327-335

Mathematics

General Topology

To appear in Topology and its Applications

Scientific paper

Let $f: X\times K\to \mathbb R$ be a separately continuous function and $\mathcal C$ a countable collection of subsets of $K$. Following a result of Calbrix and Troallic, there is a residual set of points $x\in X$ such that $f$ is jointly continuous at each point of $\{x\}\times Q$, where $Q$ is the set of $y\in K$ for which the collection $\mathcal C$ includes a basis of neighborhoods in $K$. The particular case when the factor $K$ is second countable was recently extended by Moors and Kenderov to any \v{C}ech-complete Lindel\"of space $K$ and Lindel\"of $\alpha$-favorable $X$, improving a generalization of Namioka's theorem obtained by Talagrand. Moors proved the same result when $K$ is a Lindel\"of $p$-space and $X$ is conditionally $\sigma$-$\alpha$-favorable space. Here we add new results of this sort when the factor $X$ is $\sigma_{C(X)}$-$\beta$-defavorable and when the assumption "base of neighborhoods" in Calbrix-Troallic's result is replaced by a type of countable completeness. The paper also provides further information about the class of Namioka spaces.

Affiliated with

Also associated with

No associations

Rating

Some results on separate and joint continuity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Some results on separate and joint continuity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some results on separate and joint continuity will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-428593