Bibliography

1

Emilio Acerbi, Luciano Modica, and Sergio Spagnolo. Problemi scelti di Analisi Matematica II. Liguori Editore, 1986. ISBN 88-207-1484-1.

2

L. Ambrosio, C. Mantegazza, and F. Ricci. Complementi di matematica. Scuola Normale Superiore, 2021. ISBN 9788876426933. URL https://books.google.it/books?id=1QR0zgEACAAJ.

3

T. M. Apostol. Mathematical Analysis. Addison - Wesley, 1974.

4

T.M. Apostol. Calculus, Volume 1. Wiley, 1991. ISBN 9780471000051. URL https://books.google.it/books?id=o2D4DwAAQBAJ.

5

John L. Bell. The Axiom of Choice. In Edward N. Zalta, editor, The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, Winter 2021 edition, 2021.

6

Andreas Blass. Existence of bases implies the axiom of choice. In Axiomatic set theory (Boulder, Colo., 1983), volume 31 of Contemp. Math., pages 31–33. Amer. Math. Soc., Providence, RI, 1984.

7

H. Cartan. Elementary Theory of Analytic Functions of One or Several Complex Variables. Dover Books on Mathematics. Dover Publications, 2013. ISBN 9780486318677. URL https://books.google.it/books?id=xUHDAgAAQBAJ.

8

Mariano Giaquinta and Giuseppe Modica. Analisi Matematica 1. Funzioni di una variabile. Pitagora Editrice Bologna, 1999. ISBN 9788837110499.

9

P.R. Halmos. Naive Set Theory. Undergraduate Texts in Mathematics. Springer New York, 2013. ISBN 9781475716450. URL https://books.google.it/books?id=jV_aBwAAQBAJ.

10

H. Herrlich. Axiom of Choice. Axiom of Choice. Springer, 2006. ISBN 9783540309895. URL https://books.google.it/books?id=JXIiGGmq4ZAC.

11

D. Hilbert, E.J. Townsend, and E. Jerome. The Foundations of Geometry. Project Gutenberg. Project Gutenberg., 2004. URL https://www.gutenberg.org/ebooks/17384.

12

P.G. Hinman. Fundamentals of Mathematical Logic. Taylor & Francis, 2005. ISBN 9781568812625. URL https://books.google.it/books?id=xA6D8o72qAgC.

13

T. Jech. Set Theory: The Third Millennium Edition, revised and expanded. Springer Monographs in Mathematics. Springer Berlin Heidelberg, 2007. ISBN 9783540447610. URL https://books.google.it/books?id=CZb-CAAAQBAJ.

14

J.L. Kelley. General Topology. Graduate Texts in Mathematics. Springer New York, 1975. ISBN 9780387901251. URL https://books.google.it/books?id=-goleb9Ov3oC.

15

Steven G. Krantz. The Axiom of Choice, pages 121–126. Birkhäuser Boston, Boston, MA, 2002. ISBN 978-1-4612-0115-1. DOI: 10.1007/978-1-4612-0115-1_9.

16

Azriel Levy. The independence of various definitions of finiteness. Fundamenta Mathematicae, 46:1–13, 1958. DOI: 10.4064/fm-46-1-1-13. URL https://api.semanticscholar.org/CorpusID:118218255.

17

G. H. Meisters. Polygons have ears. The American Mathematical Monthly, 82(6):648–651, 1975. ISSN 00029890, 19300972. DOI: 10.2307/2319703.

18

Jan Mycielski. A system of axioms of set theory for the rationalists. volume 53, pages 206–213, 2006. URL https://www.ams.org/journals/notices/200602/200602FullIssue.pdf.

19

Livio C. Piccinini, Giovanni Vidossich, and Guido Stampacchia. Equazioni differenziali ordinarie in \(R^ N\) (problemi e metodi). Liguori Editore, 1978.

20

to3em. Ordinary Differential Equations in Rn. Springer, 1984. ISBN 978-0-387-90723-9. DOI: 10.1007/978-1-4612-5188-0.

21

H. Rubin and J.E. Rubin. Equivalents of the Axiom of Choice, II. ISSN. Elsevier Science, 1985. ISBN 9780080887654. URL https://books.google.it/books?id=LSsbBU9FesQC.

22

Walter Rudin. Principles of Mathematical Analysis. McGraw–Hill, New York, 3rd edition, 1964.

23

Alfred Tajtelbaum-Tarski. Sur quelques théorèmes qui équivalent à l’axiome du choix. Fundamenta Mathematicae, 5(1):147–154, 1924.

24

A. E. Taylor. L’hospital’s rule. The American Mathematical Monthly, 59(1):20–24, 1952. ISSN 00029890, 19300972. URL http://www.jstor.org/stable/2307183.

25

Gerald Teschl. Ordinary differential equations and dynamical systems, volume 140. American Mathematical Soc., 2012. ISBN 978-0-8218-8328-0. URL http://www.mat.univie.ac.at/~gerald/ftp/book-ode/index.html. (Freely available on the author’s website).

26

Helge Tverberg. A proof of the jordan curve theorem. Bulletin of the London Mathematical Society, 12(1):34–38, 1980. DOI: 10.1112/blms/12.1.34.

27

Wikipedia. Mathematical morphology — Wikipedia, the free encyclopedia, 2016. URL https://en.wikipedia.org/w/index.php?title=Mathematical_morphology&oldid=714099245. [Online; accessed 24-July-2016].

28

to3em. Naive set theory — Wikipedia, the free encyclopedia, 2016. URL https://en.wikipedia.org/w/index.php?title=Naive_set_theory&oldid=740668523. [Online; accessed 22-September-2016].

29

to3em. Tautologia — Wikipedia, l’enciclopedia libera, 2016. URL http://it.wikipedia.org/w/index.php?title=Tautologia&oldid=81165325. [Online; in data 29-luglio-2016].

30

to3em. Zermelo–Fraenkel set theory — Wikipedia, the free encyclopedia, 2016. URL https://en.wikipedia.org/w/index.php?title=Zermelo-Fraenkel_set_theory&oldid=745042010. [Online; accessed 18-October-2016].

31

to3em. Strictly convex space — Wikipedia, the free encyclopedia, 2018. URL https://en.wikipedia.org/w/index.php?title=Strictly_convex_space&oldid=861198993. [Online; accessed 15-maggio-2023].

32

to3em. Ordered ring — Wikipedia, the free encyclopedia, 2021. URL https://en.wikipedia.org/w/index.php?title=Ordered_ring&oldid=1035305291. [Online; accessed 16-November-2022].

33

to3em. Two ears theorem — Wikipedia, the free encyclopedia, 2021. URL https://en.wikipedia.org/w/index.php?title=Two_ears_theorem&oldid=1024888322. [Online; accessed 13-novembre-2022].

34

to3em. Accumulation point — Wikipedia, the free encyclopedia, 2022. URL https://en.wikipedia.org/w/index.php?title=Accumulation_point&oldid=1097360512. [Online; accessed 29-dicembre-2022].

35

to3em. Bézout’s identity — Wikipedia, the free encyclopedia, 2022. URL https://en.wikipedia.org/w/index.php?title=Bezout_s_identity&oldid=1123826021. [Online; accessed 30-novembre-2022].

36

to3em. Cantor’s intersection theorem — Wikipedia, the free encyclopedia, 2022. URL https://en.wikipedia.org/w/index.php?title=Cantor's_intersection_theorem&oldid=1127277305. [Online; accessed 28-giugno-2023].

37

to3em. Derivazione delle funzioni iperboliche — Wikipedia, l’enciclopedia libera, 2022. URL http://it.wikipedia.org/w/index.php?title=Derivazione_delle_funzioni_iperboliche&oldid=128089918. [Online; in data 23-luglio-2023].

38

to3em. Directed set — Wikipedia, the free encyclopedia, 2022. URL https://en.wikipedia.org/w/index.php?title=Directed_set&oldid=1103032969. [Online; accessed 25-novembre-2022].

39

to3em. Hurwitz’s theorem (composition algebras) — Wikipedia, the free encyclopedia, 2022. URL https://en.wikipedia.org/w/index.php?title=Hurwitz's_theorem_(composition_algebras)&oldid=1092800573. [Online; accessed 14-novembre-2022].

40

to3em. Hurwitz’s theorem (number theory) — Wikipedia, the free encyclopedia, 2022. URL https://en.wikipedia.org/w/index.php?title=Hurwitz's_theorem_(number_theory)&oldid=1116947319. [Online; accessed 30-novembre-2022].

41

to3em. Integral domain — Wikipedia, the free encyclopedia, 2022. URL https://en.wikipedia.org/w/index.php?title=Integral_domain&oldid=1100509750. [Online; accessed 16-novembre-2022].

42

to3em. Net (mathematics) — Wikipedia, the free encyclopedia, 2022. URL https://en.wikipedia.org/w/index.php?title=Net_(mathematics)&oldid=1126499187. [Online; accessed 14-dicembre-2022].

43

to3em. Preorder — Wikipedia, the free encyclopedia, 2022. URL https://en.wikipedia.org/w/index.php?title=Preorder&oldid=1119474547. [Online; accessed 1-dicembre-2022].

44

to3em. Resultant — Wikipedia, the free encyclopedia, 2022. URL https://en.wikipedia.org/w/index.php?title=Resultant&oldid=1105451284. [Online; accessed 1-dicembre-2022].

45

to3em. Topologist’s sine curve — wikipedia, the free encyclopedia, 2022. URL https://en.wikipedia.org/w/index.php?title=Topologist_s_sine_curve&oldid=1116036369. [Online; accessed 24-aprile-2023].

46

to3em. Axiom of choice — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Axiom_of_choice&oldid=1173520442. [Online; accessed 28-September-2023].

47

to3em. Baire space — wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Baire_space&oldid=1138972422. [Online; accessed 3-May-2023].

48

to3em. Baker–Campbell–Hausdorff formula — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Baker-Campbell-Hausdorff_formula&oldid=1168221703. [Online; accessed 7-agosto-2023].

49

to3em. Base (topology) — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Base_(topology)&oldid=1169174814. [Online; accessed 8-agosto-2023].

50

to3em. Big O notation — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Big_O_notation&oldid=1161509085. [Online; accessed 24-giugno-2023].

51

to3em. Cantor set — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Cantor_set&oldid=1166344861. [Online; accessed 10-agosto-2023].

52

to3em. Classification of discontinuities — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Classification_of_discontinuities&oldid=1152938341. [Online; accessed 18-maggio-2023].

53

to3em. Determinant — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Determinant&oldid=1169031704. [Online; accessed 10-agosto-2023].

54

to3em. Faà di Bruno’s formula — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Faa_di_Bruno_s_formula&oldid=1160739646. [Online; accessed 19-giugno-2023].

55

to3em. General Leibniz rule — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=General_Leibniz_rule&oldid=1154019139. [Online; accessed 19-giugno-2023].

56

to3em. Heine–Borel theorem — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Heine-Borel_theorem&oldid=1163059145. [Online; accessed 7-agosto-2023].

57

to3em. Hermite interpolation — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Hermite_interpolation&oldid=1131496413. [Online; accessed 2-luglio-2023].

58

to3em. Koch snowflake — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Koch_snowflake&oldid=1143670172. [Online; accessed 4-May-2023].

59

to3em. L’Hôpital’s rule — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=L'Hopital's_rule&oldid=1174053538. [Online; accessed 16-September-2023].

60

to3em. Mazur–Ulam theorem — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Mazur-Ulam_theorem&oldid=1169902092. [Online; accessed 29-August-2023].

61

to3em. Mean value theorem — Wikipedia, the free encyclopedia. https://en.wikipedia.org/w/index.php?title=Mean_value_theorem&oldid=1164447679, 2023. [Online; accessed 16-September-2023].

62

to3em. Natural density — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Natural_density&oldid=1152033872. [Online; accessed 7-agosto-2023].

63

to3em. P-adic valuation — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=P-adic_valuation&oldid=1143204153. [Online; accessed 3-maggio-2023].

64

to3em. Polygon — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Polygon&oldid=1165846958. [Online; accessed 10-agosto-2023].

65

to3em. Rank (linear algebra) — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Rank_(linear_algebra)&oldid=1142781860. [Online; accessed 10-agosto-2023].

66

to3em. Taylor’s theorem — Wikipedia, the free encyclopedia, 2023. URL https://en.wikipedia.org/w/index.php?title=Taylor's_theorem&oldid=1174353983. [Online; accessed 16-September-2023].

67

Laurent Younes, Peter W. Michor, Jayant Shah, and David Mumford. A metric on shape space with explicit geodesics. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 19(1):25–57, 2008. ISSN 1120-6330. DOI: 10.4171/RLM/506.