Continuous Functions on an Interval
Intervals are convex (4.1.4) and closed intervals are compact (4.5.4); these special properties of intervals are reflected in special properties of continuous functions defined on them. Applications include the construction of n’th roots, a characterization of injectivity (§6.4) and automatic continuity of inverse functions (§6.5).
KeywordsContinuous Function Inverse Function Closed Interval Large Element Uniform Continuity
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