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, …
Proof that the continuous image of a compact set is compact
I know that the image of a continuous function is bounded, but I'm having trouble when it comes to prove this for vectorial functions. If somebody could help me with a step-to-step proof, that …
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 …
Continuous versus differentiable - Mathematics Stack Exchange
A function is "differentiable" if it has a derivative. A function is "continuous" if it has no sudden jumps in it. Until today, I thought these were merely two equivalent definitions of the same c...
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 …
calculus - What is the difference between continuous derivative …
What is the difference between continuous derivative and derivative? According to my teacher's solution to the assignment, it seems there exits a difference between continuous derivative …
calculus - Is there a shorthand or symbolic notation for ...
In basic calculus an analysis we end up writing the words "continuous" and "differentiable" nearly as often as we use the term "function", yet, while there are plenty of convenient (and even …
What is the difference between discrete and continuous …
Some people like discrete mathematics more than continuous mathematics, and others have a mindset suited more towards continuous mathematics - people just have different taste and …
Difference between closed and open intervals for continuous …
Intuitively, a continuous function is allowed to misbehave at the endpoints of an open interval (because it doesn't have to be defined at the endpoints), but it must behave itself on a closed …
Why is the determinant continuous? - Mathematics Stack Exchange
Here you want to refer to the topology of the latter as a normed space, which does not depend on the norm since they are all equivalent in finite dimension. Then the determinant is a polynomial …