What is a continuous extension? - Mathematics Stack Exchange
The continuous extension of f(x) f (x) at x = c x = c makes the function continuous at that point. Can you elaborate some more? I wasn't able to find very much on "continuous extension" …
Proof of Continuous compounding formula - Mathematics Stack …
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 …
What's the difference between continuous and piecewise …
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 …
Prove that the function $\\sqrt x$ is uniformly continuous on …
Nov 17, 2013 · @user1742188 It follows from Heine-Cantor Theorem, that a continuous function over a compact set (In the case of , compact sets are closed and bounded) is uniformly …
Proving the inverse of a continuous function is also continuous
6 All metric spaces are Hausdorff. Given a continuous bijection between a compact space and a Hausdorff space the map is a homeomorphism. Proof: We show that f f is a closed map. Let K …
Closure of continuous image of closure - Mathematics Stack …
Nov 14, 2012 · Closure of continuous image of closure Ask Question Asked 12 years, 8 months ago Modified 12 years, 8 months ago
calculus - Is there a shorthand or symbolic notation for ...
If it is k k times differentiable and that k k -th derivative is continuous, one writes f ∈Ck(X, Y). f ∈ C k (X, Y) I don't think there is a common notation for a function which is differentiable, but …
general topology - A map is continuous if and only if for every set ...
Nov 18, 2015 · Then f f is continuous if and only if f(A¯¯¯¯) ⊆f(A)¯ ¯¯¯¯¯¯¯¯¯ f (A) ⊆ f (A), where A¯¯¯¯ A denotes the closure of an arbitrary set A A. Assuming f f is continuous, the result is …
Topological properties preserved by continuous maps
You'll find topological properties with indication of whether they are preserved by (various kinds of) continuous maps or not (such as open maps, closed maps, quotient maps, perfect maps, …
complex analysis - Continuous determination of the argument ...
Nov 29, 2024 · Now my question is, is this a continuous determination of the argument or if no could you help me do define the argument continuously and maybe give some reference …