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I'm looking for an exercise book on real analysis which is very rigorous and that stresses the importance of the topological aspects of the subject, meaning that I would like it to have lots of exercises on the research of internal points, accumulation points, boundary points and also lots of exercises in which the task is that of finding $sup$ and $inf$ of a set described by a sequence. Difficult exercises on series would be appreciated.

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You can download free the "problem and solution" book from any public source. 1.Rami shakarchi, pro. and solutions in undergraduate analysis.

  1. B.m.makarov,M.G.Goruzina,A.A.Lodkin,A.N.Podkorytov, Selected problems in real analysis. 3.Asuman.G.Aksoy, Mohammed.A.Khamsi, a problem book in real analysis.