On a theorem of Baire about lower semicontinuous functions. (English) Zbl 1224.41062
Summary: A theorem of Baire concerning the approximation of lower semicontinuous real valued functions defined on a metric space by increasing sequences of continuous functions is extended to the “nonsymmetric” case, i.e., to quasi-metric spaces.
MSC:
| 41A30 | Approximation by other special function classes |
| 26A15 | Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable |
| 26A16 | Lipschitz (Hölder) classes |
| 26A21 | Classification of real functions; Baire classification of sets and functions |
| 54E25 | Semimetric spaces |
