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") simultaneously …

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 piecewise continuous

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 uniformly …

Following is the formula to calculate continuous compounding A = P e^(RT) Continuous Compound Interest Formula where, P = principal amount (initial investment) r = annual interest rate (as 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?

Sep 30, 2020 · The proof of the statement relies on showing that continuous functions defined in an interval are uniformly continuous. As i finished doing that part, I started wondering: what are all the …

Jun 6, 2015 · In my mind it seems to say, if a function is continuous, we can show that if it is also differentiable, then it is continuous. Rather than what I was expecting, namely, if a function is …

I was reading through Munkres' Topology and in the section on Continuous Functions, these three statements came up: If a function is continuous, open, and bijective, it is a homeomorphism. If a

Nov 14, 2012 · Closure of continuous image of closure Ask Question Asked 13 years ago Modified 13 years ago

Nov 17, 2013 · @user1742188 It follows from Heine-Cantor Theorem, that a continuous function over a compact set (In the case of $\mathbb {R}$, compact sets are closed and bounded) is uniformly …