On some conditions which imply the continuity of almost all sections \(x\rightarrow f(t,x)\). (English) Zbl 0817.26002

Grande, Zbigniew

Math. Bohem. 119, No. 1, 49-56 (1994).

The author introduces some conditions analogous to the condition \((a_ 0)\) published by him previously. With the assumptions connected with these conditions, the author investigates the continuity and quasi- continuity of almost all sections of a function \(f: I\times X\to Y\), where \(I\) is an open interval, \(Y\) a metric space and \(X\) a topological space.

Reviewer: R.Pawlak (Łódź)

MSC:

26B05	Continuity and differentiation questions
28A10	Real- or complex-valued set functions
54C08	Weak and generalized continuity

Keywords:

Lebesgue measure; density; Baire property; category; continuity; quasi- continuity; sections