· 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 example $ (0,1)\to [0,1]$ is not closed. · 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 uniformly continuous on $\mathbb r$. 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 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. · 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 $d$. The reason for using ap calculus instead of just calculus is to ensure that advanced stuff is filtered out.
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· in fact, it turns out that every continuous function from a path connected space to $\mathbb r$ is a quotient map note that the...