uniform convergence in a sentence

Examples

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