Aug 19, 2022 · The function ƒ (x) = 1/x (Figure 2.41) is a continuous function because it is continuous at every point of its domain. The point x = 0 is not in the domain of the function ƒ, so ƒ is not continuous …

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 30, 2019 · I have a very basic problem. I am confused about "continuous function" term. What really is a continuous function? A function that is continuous for all of its domain or for all real numbers? Le...

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 singular continuous …

Jul 22, 2010 · I believe that the set of all R → R continuous functions is c, the cardinality of the continuum. However, I read in the book "Metric spaces" by Ó Searcóid that set of all [0, 1] → R …

Mar 7, 2013 · 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 like …

Apr 12, 2024 · Fixed point for some continuous function. Ask Question Asked 1 year, 8 months ago Modified 1 year, 8 months ago

Hölder- continuous function [duplicate] Ask Question Asked 12 years, 7 months ago Modified 9 years, 5 months ago

Sep 16, 2012 · Then strongly continuous is the same as continuous (in the usual sense) hence an example of a (strongly) continuous function would for example be f(x) = x2 f (x) = x 2. An example of …

Dec 25, 2016 · The tangent function is continuous on its domain; it isn’t a continuous function on R R simply because it isn’t defined on all of R R (and moreover, the discontinuities aren’t even removable).