Jun 11, 2025 · 6 "Every metric is continuous" means that a metric $d$ on a space $X$ is a continuous function in the topology on the product $X \times X$ determined by $d$.

As you have it written now, you still have to show $\sqrt {x}$ is continuous on $ [0,a)$, but you are on the right track. As @user40615 alludes to above, showing the function is continuous at …

The containment "continuous"$\subset$"integrable" depends on the domain of integration: It is true if the domain is closed and bounded (a closed interval), false for open intervals, and for …

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 …

$f,g$ continuous from $X$ to $Y$. if they are agree on a dense set $A$ of $X$ then they agree on $X$ Ask Question Asked 12 years ago Modified 10 months ago

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, …

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 …

Dec 5, 2016 · Proof that a linear transformation is continuous Ask Question Asked 12 years, 5 months ago Modified 8 years, 10 months ago

Jul 27, 2024 · In the continuous case, where random variables can take on values on a continuous scale, the procedure is very much the same. The outcomes of experiments are …

Does a continuous mapping have to map the boundary to the boundary Ask Question Asked 7 years, 9 months ago Modified 3 years, 2 months ago