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Stillwell is the author of many textbooks and other books on mathematics including: Classical Topology and Combinatorial Group Theory, 1980, ISBN 0-387-97970-0. 2012 pbk reprint of 1993 2nd edition ISBN 978-0-387-97970-0. Mathematics and Its History, 1989, pbk reprint of 2nd edition 2002; 3rd edition 2010, ISBN 0-387-95336-1 [7]
"Analysis Situs" is a seminal mathematics paper that Henri Poincaré published in 1895. [1] Poincaré published five supplements to the paper between 1899 and 1904. [2]These papers provided the first systematic treatment of topology and revolutionized the subject by using algebraic structures to distinguish between non-homeomorphic topological spaces, founding the field of algebraic topology. [3]
Undergraduate Texts in Mathematics (UTM) (ISSN 0172-6056) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size. The books in this series tend to be written at a more elementary level than ...
Reverse Mathematics: Proofs from the Inside Out. First edition. Reverse Mathematics: Proofs from the Inside Out is a book by John Stillwell on reverse mathematics, the process of examining proofs in mathematics to determine which axioms are required by the proof. It was published in 2018 by the Princeton University Press. [1][2][3][4][5][6]
The Nielsen–Schreier theorem states that if H is a subgroup of a free group G, then H is itself isomorphic to a free group. That is, there exists a set S of elements which generate H, with no nontrivial relations among the elements of S. The Nielsen–Schreier formula, or Schreier index formula, quantifies the result in the case where the ...
In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), [2][3] also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function.
The double-rotation that identifies the walls of the lens space. In this stereographic view, the double-rotation rotates both around the z-axis and along it. A lens space is an example of a topological space, considered in mathematics. The term often refers to a specific class of 3-manifolds, but in general can be defined for higher dimensions.
Combinatorial group theory. In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations. It is much used in geometric topology, the fundamental group of a simplicial complex having in a natural and geometric way such a presentation. A very closely related ...