Titlebook: Elements of Abstract Analysis; Mícheál Ó Searcóid Textbook 2002 Springer-Verlag London 2002 calculus.compactness.convergence.functional an

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Springer Undergraduate Mathematics Serieshttp://image.papertrans.cn/e/image/307557.jpg

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https://doi.org/10.1007/1-4020-2107-0Elementary applications of the theory of convergence involve sequences in metric spaces. But there are applications of convergence techniques in non-metric spaces and there are those for which convergence of sequences does not suffice.

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Algebraic Structure,Modern analysis makes use of sets which exhibit various degrees of algebraic structure. In this chapter we shall describe the most elementary forms of that structure. Our chief concern is to articulate and formalize the algebraic properties we naturally associate with the . and . number systems.

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