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 …

Nov 14, 2012 · Closure of continuous image of closure Ask Question Asked 12 years, 11 months ago Modified 12 years, 11 months ago

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 …

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 …

Jun 12, 2016 · Basic real analysis should be a source of at least some intuition (which is misleading at times, granted). Can you think of some compact sets in $\mathbf R$? Are …

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 …

I have always treated them as the same thing. But recently, some people have told me that the two terms are different. So now I am wondering, What is the difference between …

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