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{{Math-h}}

{{Math-h}}

'''Real analysis''' is a field in [[mathematics]] that focuses on the set of [[real number]]s, their properties, [[sequence]]s and [[function]]s.  Included in this branch of mathematics are the concepts of [[Limit_%28mathematics%29|limit]]s and [[convergence]], [[calculus]], and properties of real-valued functions such as [[continuous|continuity]].  It also includes [[measure theory]].

'''Real analysis''' is a field in [[mathematics]] that focuses on the set of [[real number]]s, their properties, [[sequence]]s and [[function]]s.  Included in this branch of mathematics are the concepts of [[Limit (mathematics)|limit]]s and [[convergence]], [[calculus]], and properties of real-valued functions such as [[continuous|continuity]].  It also includes [[measure theory]].

For the purposes of this article, "analysis" will be limited to the generalization and extension of the concepts of calculus, using the concepts of elementary [[point-set topology]].

For the purposes of this article, "analysis" will be limited to the generalization and extension of the concepts of calculus, using the concepts of elementary [[point-set topology]].

The reader should be quite familiar with the concepts of calculus, especially limits and continuity.  In particular, the reader should be comfortable with the ramifications of the phrase "[[Limit_%28mathematics%29|for every epsilon]]".

The reader should be quite familiar with the concepts of calculus, especially limits and continuity.  In particular, the reader should be comfortable with the ramifications of the phrase "[[Limit (mathematics)|for every epsilon]]".

==Open sets==

==Open sets==

*[[Bolzano-Weierstrass theorem]]

*[[Bolzano-Weierstrass theorem]]

[[category:mathematics]]

[[Category:Mathematics]]