An equivalent definition of functions of the first Baire class (Q2719000)
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: An equivalent definition of functions of the first Baire class |
scientific article; zbMATH DE number 1597891
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An equivalent definition of functions of the first Baire class |
scientific article; zbMATH DE number 1597891 |
Statements
An equivalent definition of functions of the first Baire class (English)
0 references
14 May 2001
0 references
complete separable metric spaces
0 references
Baire 1 mapping
0 references
continuity
0 references
0.9112102
0 references
0.9089876
0 references
0 references
0.88859177
0 references
0.88839453
0 references
0 references
0.8840193
0 references
0.88286483
0 references
Let \(f:X \to Y\) be a mapping between complete separable metric spaces \((X,d_X)\) and \((Y,d_Y)\). Then \(f\) is of the first Baire class if and only if for each \(r > 0\) there is a function \(\eta > 0\) on \(X\) such that \(d_Y(f(x),f(y)) < r\) whenever \(d_X(x,y) < \min(\eta (x),\eta (y))\).
0 references
