000			a
999			_c33000 _d33000
008			240318b xxu||||| |||| 00| 0 eng d
020			_a9783031197376
082			_a515 _bSEC
100			_aSecchi, Simone
245			_aA circle-Line Study of Mathematical Analysis
260			_bSpringer, _c2022 _aCham :
300			_axix, 469 p. ; _bill., _c24 cm.
365			_b54.99 _c€ _d93.50
490			_aLa Matematica per il 3+2
520			_aThe book addresses the rigorous foundations of mathematical analysis. The first part presents a complete discussion of the fundamental topics: a review of naive set theory, the structure of real numbers, the topology of R, sequences, series, limits, differentiation and integration according to Riemann. The second part provides a more mature return to these topics: a possible axiomatization of set theory, an introduction to general topology with a particular attention to convergence in abstract spaces, a construction of the abstract Lebesgue integral in the spirit of Daniell, and the discussion of differentiation in normed linear spaces. The book can be used for graduate courses in real and abstract analysis and can also be useful as a self-study for students who begin a Ph.D. program in Analysis. The first part of the book may also be suggested as a second reading for undergraduate students with a strong interest in mathematical analysis.
650			_aMathematical analysis
650			_aSet theory
650			_aAccumulation point
650			_aBanach spaces
650			_aCauchy sequence
650			_aClosed set
650			_aCompact space
650			_aContinuous function
650			_aElementary functions
650			_aHausdorff space
650			_aLevi's Theorem
650			_aMeasurable functions
650			_aOpen cover
650			_aProduct topology
650			_aRiemann integra
650			_aTopological space
942			_2ddc _cBK