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  2. Topology - Wikipedia

    en.wikipedia.org/wiki/Topology

    Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing ...

  3. Counterexamples in Topology - Wikipedia

    en.wikipedia.org/wiki/Counterexamples_in_Topology

    Counterexamples in Topology (1970, 2nd ed. 1978) is a book on mathematics by topologists Lynn Steen and J. Arthur Seebach, Jr. In the process of working on problems like the metrization problem, topologists (including Steen and Seebach) have defined a wide variety of topological properties. It is often useful in the study and understanding of ...

  4. General topology - Wikipedia

    en.wikipedia.org/wiki/General_topology

    In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. The fundamental concepts in point-set ...

  5. Euler's Gem - Wikipedia

    en.wikipedia.org/wiki/Euler's_Gem

    Euler's Gem: The Polyhedron Formula and the Birth of Topology is a book on the formula for the Euler characteristic of convex polyhedra and its connections to the history of topology. It was written by David Richeson and published in 2008 by the Princeton University Press, with a paperback edition in 2012. It won the 2010 Euler Book Prize of ...

  6. A Topological Picturebook - Wikipedia

    en.wikipedia.org/wiki/A_Topological_Picturebook

    ISBN. 0387964266. A Topological Picturebook is a book on mathematical visualization in low-dimensional topology by George K. Francis. It was originally published by Springer in 1987, and reprinted in paperback in 2007. The Basic Library List Committee of the Mathematical Association of America has recommended its inclusion in undergraduate ...

  7. Filters in topology - Wikipedia

    en.wikipedia.org/wiki/Filters_in_topology

    Filters in topology. The power set lattice of the set with the upper set colored dark green. It is a filter, and even a principal filter. It is not an ultrafilter, as it can be extended to the larger proper filter by including also the light green elements. Because cannot be extended any further, it is an ultrafilter.

  8. Introduction to 3-Manifolds - Wikipedia

    en.wikipedia.org/wiki/Introduction_to_3-Manifolds

    Introduction to 3-Manifolds. First edition. Introduction to 3-Manifolds is a mathematics book on low-dimensional topology. It was written by Jennifer Schultens and published by the American Mathematical Society in 2014 as volume 151 of their book series Graduate Studies in Mathematics .

  9. A Guide to the Classification Theorem for Compact Surfaces

    en.wikipedia.org/wiki/A_Guide_to_the...

    First edition. A Guide to the Classification Theorem for Compact Surfaces is a textbook in topology, on the classification of two-dimensional surfaces. It was written by Jean Gallier and Dianna Xu, and published in 2013 by Springer-Verlag as volume 9 of their Geometry and Computing series (doi: 10.1007/978-3-642-34364-3, ISBN 978-3-642-34363-6).