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10 relations: Comparison of topologies, Continuous function, Extended real number line, Mathematics, Open set, Partially ordered set, Semi-continuity, Singleton (mathematics), Specialization (pre)order, Upper set.
Comparison of topologies
In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set.
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Extended real number line
In mathematics, the affinely extended real number system is obtained from the real number system by adding two elements: and (read as positive infinity and negative infinity respectively).
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
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Partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.
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Semi-continuity
In mathematical analysis, semi-continuity (or semicontinuity) is a property of extended real-valued functions that is weaker than continuity.
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Singleton (mathematics)
In mathematics, a singleton, also known as a unit set, is a set with exactly one element.
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Specialization (pre)order
In the branch of mathematics known as topology, the specialization (or canonical) preorder is a natural preorder on the set of the points of a topological space.
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Upper set
In mathematics, an upper set (also called an upward closed set or just an upset) of a partially ordered set (X,≤) is a subset U with the property that, if x is in U and x≤y, then y is in U. The dual notion is lower set (alternatively, down set, decreasing set, initial segment, semi-ideal; the set is downward closed), which is a subset L with the property that, if x is in L and y≤x, then y is in L. The terms order ideal or ideal are sometimes used as synonyms for lower set.
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