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What is the historical motivation of continuous functions? Also, does anyone know who first isolated the idea?

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  • $\begingroup$ According to Wikipedia (and I've read it elsewhere) topology goes back to the ideas of geometria situs (the geometry of place) and analysis situs (the picking apart of place) by Liebniz in the 17th C, unfortunately the article doesn't explain how. $\endgroup$ Nov 21, 2017 at 18:14

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Isolation of the modern concept is generally attributed to Bolzano (1817; translation) and/or Cauchy (1821), with some controversy on their independence: see Grattan-Guinness (1970), Freudenthal (1971). Kline (1972, p. 950) says Bolzano’s motivation was to rigorously prove the fundamental theorem of algebra, and on his way, the intermediate value theorem — stated in his memoir’s title.

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