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- What is a continuous extension? - Mathematics Stack Exchange
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") simultaneously with the phrase "ap calculus" The reason for using "ap calculus" instead of just "calculus" is to ensure that advanced stuff is filtered out
- Proof of Continuous compounding formula - Mathematics Stack Exchange
12 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 rate (as a decimal) t = number of years A = amount after time t The above is specific to continuous compounding
- is bounded linear operator necessarily continuous?
In general, is a bounded linear operator necessarily continuous (I guess the answer is no, but what would be a counter example?) Are things in Banach spaces always continuous?
- general topology - A map is continuous if and only if for every set . . .
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
- general topology - How can a continuous function map closed sets to . . .
So Brian M Scott, can we say is that if f is continuous AND injective, then f maps closed sets to closed sets?
- If $f,g$ are continuous functions, then $fg$ is continuous?
I believe it follows from the fact that we showed $f+g$ is continuous whenever $f$ and $g$ are continuous Indeed, if $g$ is continuous, then $-g$ is clearly continuous
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