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  2. Lindelöf's lemma - Wikipedia

    en.wikipedia.org/wiki/Lindelöf's_lemma

    Download as PDF; Printable version; ... Lindelöf's lemma is a simple but useful lemma in topology on the real line, ... M.A. Armstrong (1983), Basic Topology, ...

  3. Ambient isotopy - Wikipedia

    en.wikipedia.org/wiki/Ambient_isotopy

    M. A. Armstrong, Basic Topology, Springer-Verlag, 1983 Sasho Kalajdzievski, An Illustrated Introduction to Topology and Homotopy , CRC Press, 2010, Chapter 10: Isotopy and Homotopy This topology-related article is a stub .

  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 .

  5. Topology - Wikipedia

    en.wikipedia.org/wiki/Topology

    A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. 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 ...

  6. Simplicial homology - Wikipedia

    en.wikipedia.org/wiki/Simplicial_homology

    A key concept in defining simplicial homology is the notion of an orientation of a simplex. By definition, an orientation of a k-simplex is given by an ordering of the vertices, written as (v 0,...,v k), with the rule that two orderings define the same orientation if and only if they differ by an even permutation.

  7. Clopen set - Wikipedia

    en.wikipedia.org/wiki/Clopen_set

    As a less trivial example, consider the space of all rational numbers with their ordinary topology, and the set of all positive rational numbers whose square is bigger than 2. Using the fact that 2 {\displaystyle {\sqrt {2}}} is not in Q , {\displaystyle \mathbb {Q} ,} one can show quite easily that A {\displaystyle A} is a clopen subset of Q ...

  8. Dying To Be Free - The Huffington Post

    projects.huffingtonpost.com/dying-to-be-free...

    Sleep deprivation was supposed to act as its own mind-altering drug. Many of Dederich’s harsher prescriptions were unique to Synanon, but his basic idea — that addicts would improve themselves by punishing each other — gained currency throughout the U.S. treatment system and particularly in prisons.

  9. Homotopy - Wikipedia

    en.wikipedia.org/wiki/Homotopy

    A homotopy between two embeddings of the torus into : as "the surface of a doughnut" and as "the surface of a coffee mug".This is also an example of an isotopy.. Formally, a homotopy between two continuous functions f and g from a topological space X to a topological space Y is defined to be a continuous function: [,] from the product of the space X with the unit interval [0, 1] to Y such that ...