Given x 0 , a point of a convex subset C of a Euclidean space, the two following statements are proven to be equivalent: (i) every convex function f : C → ℝ is upper semi-continuous at x 0 , and (ii) ...

A necessary and sufficient condition is obtained for an L function to have a continuous derivative of the kth order. Other results concerning the continuity properties of infinitely divisible ...

This unit generalises some theorems about convergence and continuity from Level 1 analysis, and develops a theory of convergence in Rn and more generally in metric spaces. Topics will include basic ...

Maths 12th Continuity and Differentiability MCQs: The Central Board of Secondary Education (CBSE) holds the term-end board exams for class 12, which is considered among the top and hardest exams in ...