Ever seen the little ‘You Are Here’ dot on a map of the airport, or the mall, or any other structure? That’s a demonstration of the Brouwer Fixed-Point Theorem. Violently shaken martini shakers and ...

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) ...

In this article, you will get chapter notes of chapter Continuity and Differentiability including all important topics like continuous functions, sum, difference, product and quotient of continuous ...