I am reading Chapter 11 of Real Analysis written by Royden and Patrick (4th). It says "The concept of uniform convergence of a sequence of functions is a metric concept. The concept of pointwise convergence is NOT a metric concept." (page 222) I know the definitions for uniform and pointwise convergence of a sequence of functions. However, I could not understand the quote above. Could anyone explain it to me, please? Thank you!
2026-04-13 19:14:19.1776107659
Difference between Metric Space and Topological Space
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