Topological & Functional-Analytic Spaces

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Abstractions about classes of topological and functional-analytic spaces, including separation axioms, convexity and metrizability conditions, cones and boundaries, used to distinguish spaces by their topological or normed-space properties.

13 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Absolutely convex set — In mathematics, a subset C of a real or complex vector space is said to be absolutely convex or disked if it is convex and balanced (some people use the term "circled" instead of "balanced"), in which case it is called a disk.
• Cellular space — A cellular space is a compact Hausdorff space that has the structure of a CW complex.
• Completely regular space — In topology and related branches of mathematics, Tychonoff spaces and completely regular spaces are kinds of topological spaces.
• Cone (topology) — In topology, especially algebraic topology, the cone of a topological space X is intuitively obtained by stretching X into a cylinder and then collapsing one of its end faces to a point.
• Hereditarily normal space — In topology and related branches of mathematics, a normal space is a topological space in which any two disjoint closed sets have disjoint open neighborhoods.
• K-space (functional analysis) — In mathematics, more specifically in functional analysis, a K-space is an F-space V such that every extension of F-spaces (or twisted sum) of the form.
• Metrizable topological vector space — In functional analysis and related areas of mathematics, a metrizable (resp. pseudometrizable) topological vector space (TVS) is a TVS whose topology is induced by a metric (resp. pseudometric).
• Minkowski space (number field) — In mathematics, specifically the field of algebraic number theory, a Minkowski space is a Euclidean space associated with an algebraic number field.
• T0 space — In topology and related branches of mathematics, a topological space X is a T 0 space or Kolmogorov space (named after Andrey Kolmogorov) if for every pair of distinct points of X, at least one of them has a neighborhood not containing the other.
• T4 Space — In topology and related branches of mathematics, a normal space is a topological space in which any two disjoint closed sets have disjoint open neighborhoods.
• Topological Algebra — In mathematics, a topological algebra A is an algebra and at the same time a topological space, where the algebraic and the topological structures are coherent in a specified sense.
• Topological Boundary — In topology and mathematics in general, the boundary of a subset of a topological space is the set of points in the closure of not belonging to the interior of .
• Type and Cotype of a Banach Space — In functional analysis, the type and cotype of a Banach space are a classification of Banach spaces through probability theory and a measure for how far a Banach space is away from being a Hilbert space.