4
votes
0answers
155 views

Well-founded families of sets and topological convergence

Background/Motivation A space is scattered if every non-empty subset has an isolated point. A space is pseudoradial if every non-closed set contains a transfinite sequence (a well-ordered net) ...
1
vote
0answers
170 views

convergence of sets and limit of an integral

Let $X\subset\mathbb{R}$ and $Y\subset\mathbb{R}$ be compact sets. Let $f:X\times Y\rightarrow\mathbb{R}$ be a $C^{1}$ function. Let $s:Y\rightarrow X$ be a function (not necessarily continuous). ...