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 …

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 …

May 6, 2016 · A constant function is continuous, but for most topologies does not map an open set to an open set. For a familiar somewhat different example, the image of $ (0,42)$ under …

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 …

Apr 27, 2021 · Continuous from the left/right Ask Question Asked 4 years, 6 months ago Modified 4 years, 6 months ago

In either case, a function is continuous on its domain if it is continuous at every point in the domain. Thus a function can be continuous on either $ [a,b]$ or $ (a,b)$.

Continuous function proof by definition Ask Question Asked 12 years, 7 months ago Modified 6 years, 5 months ago

Mar 7, 2013 · 21 I am self-studying general topology, and I am curious about the definition of the continuous function. I know that the definition derives from calculus, but why do we define it …