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I know that the image of a continuous function is bounded, but im having trouble when it comes to prove this for vectorial functions. The authors prove the proposition that every proper convex function defined on a finite-dimensional separated topological linear space is continuous on the interior of its effective domain. 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) … · youll need to complete a few actions and gain 15 reputation points before being able to upvote. · now my question is, is this a continuous determination of the argument or if no could you help me do define the argument continuously and maybe give some reference where … · 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 … · a continuous function is a function where the limit exists everywhere, and the function at those points is defined to be the same as the limit. I was looking at the image of a … Are continuous … · basic real analysis should be a source of at least some intuition (which is misleading at times, granted). · closure and continuous map ask question asked 6 years, modified 6 years, Upvoting indicates when questions and answers are useful. Whats reputation … 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 If somebody could help me with a step-to-step proof, that … Can you think of some compact sets in $\mathbf r$?