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Line 1: − {{merge|calculus}}+ +
added an overall introduction that touches on calculus, advanced calculus, and topology; improvements welcome
'''Continuity''' is a concept central to [[calculus]], [[advanced calculus]] and [[topology]]. In calculus, continuity is defined based on limits. In advanced calculus, continuity is defined using neighborhoods or sequences. In topology, a function is continuous if the inverse image of every open set in the function's range is also an open set in the function's domain. In all three fields of [[mathematics]], the unifying characteristic of continuity is that points near each other in a set or domain are mapped by the continuous function to points that are near each other in the corresponding set or range.
In [[calculus]], a [[function]] ''f(x)'' is said to be '''continuous''' at point ''c'' if ''f(c)'' equals the limit of ''f(x)'' as x approaches c from both the positive and negative directions.
In [[calculus]], a [[function]] ''f(x)'' is said to be '''continuous''' at point ''c'' if ''f(c)'' equals the limit of ''f(x)'' as x approaches c from both the positive and negative directions.