topological collection

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• Topological space — Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion. The… …   Wikipedia

• Topological data analysis — is a new area of study aimed at having applications in areas such as data mining and computer vision. The main problems are (1) how one infers high dimensionalstructure from low dimensional representations; and (2) how one assembles discrete… …   Wikipedia

• Topological group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• Topological game — A topological game is an infinite positional game of perfect information played between two players on a topological space. Players choose objects with topological properties such as points, open sets, closed sets and open coverings. Time is… …   Wikipedia

• Topological index — For topological index in mathematics, see Atiyah–Singer index theorem. In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index also known as a connectivity index is a type of a molecular… …   Wikipedia

• topological space — Math. a set with a collection of subsets or open sets satisfying the properties that the union of open sets is an open set, the intersection of two open sets is an open set, and the given set and the empty set are open sets. [1945 50] * * *… …   Universalium

• topological space — noun Date: 1926 a set with a collection of subsets satisfying the conditions that both the empty set and the set itself belong to the collection, the union of any number of the subsets is also an element of the collection, and the intersection of …   New Collegiate Dictionary

• topological space — noun a) A set, together with a collection of its subsets that form a topology on the set. b) The set itself …   Wiktionary

• Locally finite collection — In the mathematical field of topology, local finiteness is a property of collections of subsets of a topological space. It is fundamental in the study of paracompactness and topological dimension. A collection of subsets of a topological space X… …   Wikipedia

• Characterizations of the category of topological spaces — In mathematics, a topological space is usually defined in terms of open sets. However, there are many equivalent characterizations of the category of topological spaces. Each of these definitions provides a new way of thinking about topological… …   Wikipedia

• Locally convex topological vector space — In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… …   Wikipedia