TITLE:
A Remark on the Uniform Convergence of Some Sequences of Functions
AUTHORS:
Guy Degla
KEYWORDS:
Sequence of Functions, Uniform Convergence, Metric, Boundedness
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.5 No.9,
July
6,
2015
ABSTRACT: We stress a basic criterion that shows in a simple way how a sequence of real-valued functions can converge uniformly when it is more or less evident that the sequence converges uniformly away from a finite number of points of the closure of its domain. For functions of a real variable, unlike in most classical textbooks our criterion avoids the search of extrema (by differential calculus) of their general term.