On discontinuity points for closed graph functions (Q909810)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On discontinuity points for closed graph functions |
scientific article; zbMATH DE number 4138071
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On discontinuity points for closed graph functions |
scientific article; zbMATH DE number 4138071 |
Statements
On discontinuity points for closed graph functions (English)
0 references
1990
0 references
The main result of the paper states: Let g: \(R\to R\) (R - the real line) be continuous. Then the following statements are equivalent: (i) for each closed graph function \(f: R\to R\) the composite function g(f) is quasicontinuous; (ii) for each open set V in R such that \(g^{-1}(V)\neq \emptyset,\) \(\sup g^{-1}(V)=\infty\) and \(\inf g^{-1}(V)=-\infty.\)
0 references
discontinuity points
0 references
closed graph function
0 references
0.8045557737350464
0 references
