topological space

Definitions of topological space
  1. noun
    (mathematics) any set of points that satisfy a set of postulates of some kind
    “assume that the topological space is finite dimensional”
    synonyms: mathematical space
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    subspace
    a space that is contained within another space
    null space
    a space that contains no points; and empty space
    manifold
    a set of points such as those of a closed surface or an analogue in three or more dimensions
    metric space
    a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality
    Euclidean space
    a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional
    Hilbert space
    a metric space that is linear and complete and (usually) infinite-dimensional
    type of:
    infinite, space
    the unlimited expanse in which everything is located
    set
    (mathematics) an abstract collection of numbers or symbols
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