Connection - Mathematics


  • Connection (mathematics), a way of specifying a derivative of a geometrical object along a vector field on a manifold
    • Levi-Civita connection, used in differential geometry and general relativity; differentiates a vector field along another vector field
    • Connection (vector bundle), differentiates a section of a vector bundle along a vector field
    • Connection form, a manner of specifying a connection using differential forms
    • Connection (principal bundle), gives the derivative of a section of a principle bundle
    • Ehresmann connection, gives a manner for differentiating sections of a general fibre bundle
    • Cartan connection, achieved by identifying tangent spaces with the tangent space of a certain model Klein geometry
  • Connectedness, a property of topological space, graph or category (with different meanings)
    • Connected category, a category for which, for every two objects, there is at least one morphism connecting them
    • Connected space, a topological space which cannot be written as the disjoint union of two or more nonempty open spaces
    • Connectivity (graph theory)
    • Pixel connectivity
    • Connected sum
  • Galois connection, a type of correspondence between two partially ordered sets
  • Connection (algebraic framework)

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Famous quotes containing the word mathematics:

    Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.
    Simone Weil (1909–1943)

    The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.
    Willard Van Orman Quine (b. 1908)