To find examples and explanations on the internet at the elementary calculus level, try googling the phrase "continuous extension" (or variations of it, such as "extension by continuity") …

Oct 15, 2016 · A continuous function is a function where the limit exists everywhere, and the function at those points is defined to be the same as the limit. I was looking at the image of a …

Jan 27, 2014 · To understand the difference between continuity and uniform continuity, it is useful to think of a particular example of a function that's continuous on $\mathbb R$ but not …

May 10, 2019 · Continue to help good content that is interesting, well-researched, and useful, rise to the top! To gain full voting privileges,

3 This property is unrelated to the completeness of the domain or range, but instead only to the linear nature of the operator. Yes, a linear operator (between normed spaces) is bounded if …

Proving the inverse of a continuous function is also continuous Ask Question Asked 11 years, 11 months ago Modified 7 years, 10 months ago

Jan 24, 2015 · Note the ending "-ly", which makes it an adverb, not an adjective. So "continuously differentiable" means "differentiable in a continuous way".

Oct 16, 2013 · Continuous Compositions: Thm: The composite denoted by, “•”, of two continuous functions is continuous. Pf/Let f:A—>B and g:C—>D be continuous functions : g (A) C A.

Sep 16, 2021 · I am self-learning Real Analysis from the text Understanding Analysis by Stephen Abbott. I'd like someone to verify if my proofs/counterexamples to below exercise are rigorous …

Dec 10, 2017 · If not all continuous functions are differentiable, so how is it that all continuous functions have anti-derivatives?