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 12 years 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".

Jul 30, 2014 · Continuous Spectrum: The continuous spectrum exists wherever $\omega (\lambda)$ is positive, and you can see the reason for the original use of the term continuous …

May 13, 2012 · A uniform continuous function which is not Hölder continuous Ask Question Asked 13 years, 5 months ago Modified 7 years, 5 months ago

Jun 6, 2015 · That the determinant is a continuous function. Is this proof you've provided available in a textbook somewhere?