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") …

May 10, 2019 · Of course, the CDF of the always-zero random variable $0$ is the right-continuous unit step function, which differs from the above function only at the point of discontinuity at $x=0$.

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 …

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 …

Nov 9, 2024 · I learned a theorem that if $f$ is continuous and bijective then $f^ {-1}$ is continuous. I went online to search for a proof and saw a really long proof in this link.

Jan 13, 2012 · the difference is in definitions, so you may want to find an example what the function is continuous in each argument but not jointly

Proving the inverse of a continuous function is also continuous Ask Question Asked 12 years, 1 month ago Modified 8 years ago

A function f: [0,1]→ R f: [0, 1] → R is called singular continuous, if it is nonconstant, nondecreasing, continuous and f(t) = 0 f (t) = 0 whereever the derivative exists. Let f f be a …

In general, is a bounded linear operator necessarily continuous (I guess the answer is no, but what would be a counter example?) Are things in Banach spaces always continuous?

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