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1 / 5 2 / 5 3 / 5 4 / 5 5 / 5 ❮ ❯ I know that the image of a continuous function is bounded, but im having trouble when it comes to prove this for vectorial functions. 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 … · closure of continuous image of closure ask question asked 12 years, modified 12 years, If somebody could help me with a step-to-step proof, that … One thing to note is that tao is only talking … 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) … Proving the inverse of a continuous function is also continuous ask question asked 11 years, modified 7 years, · in fact, it turns out that every continuous function from a path connected space to $\mathbb r$ is a quotient map note that the closed map lemma cannot be generalised, for … Im interested in a … · 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 $d$. · of course having two variables introduces a few more details, but they are straightforward once you understand the idea. · to understand the difference between continuity and uniform continuity, it is useful to think of a particular example of a function thats continuous on $\mathbb r$ but not … · let z = x + iy z = x + i y be any complex number, then in general the argument of z z, i. e. Arg(z) arg (z) is not continuous since it has jumps of 2π 2 π. ...
