Real Analysis: Topology of the Real Line
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All Real AnalysisSets and Logic FoundationsCardinality and CountabilityReal Numbers and CompletenessSequences and ConvergenceLimit Superior and Bolzano WeierstrassSeries and Convergence TestsLimits and Continuity of FunctionsUniform Continuity and Extreme Value TheoremsDifferentiation and Mean Value TheoremRiemann Integration and Fundamental TheoremSequences of Functions and Uniform ConvergencePower Series and Approximation TheoremsTopology of the Real Line
Determine the boundary of the set within the real number metric space, where the metric is the standard distance function.
Prove that the real numbers and the empty set are open sets.
Explain why a closed interval, such as , is not an open set.