Monotone and discrete limits of continuous functions. (English) Zbl 1011.26003

The author investigates some topological spaces \(X\) such that each upper semi-continuous real function on \(X\), which is the discrete limit of a sequence of continuous functions, is also the disrete limit of a decreasing sequence of continuous functions.


26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
26A03 Foundations: limits and generalizations, elementary topology of the line
26A21 Classification of real functions; Baire classification of sets and functions