31. Uniform convergence is desirable for a series because many properties of the terms of the series are then retained by the limit.32. Then is dense in ( given the topology of uniform convergence ) if and only if it separates points and vanishes nowhere. 33. The Dirichlet series case is more complicated, though : absolute convergence and uniform convergence may occur in distinct half-planes. 34. It is a remarkable fact, fundamental to the theory of univalent functions, that univalence is essentially preserved under uniform convergence . 35. :If I'm not missing something, uniform convergence and talk ) 08 : 10, 20 February 2009 ( UTC) 36. In the above step, we were able to interchange the integral and the limit because of the uniform convergence of the integrand. 37. *PM : limit laws for uniform convergence , id = 7215-- WP guess : limit laws for uniform convergence-- Status: 38. *PM : limit laws for uniform convergence, id = 7215-- WP guess : limit laws for uniform convergence -- Status: 39. *PM : point preventing uniform convergence , id = 9837 new !-- WP guess : point preventing uniform convergence-- Status: 40. *PM : point preventing uniform convergence, id = 9837 new !-- WP guess : point preventing uniform convergence -- Status:
