What does pointclass mean?

Definitions for pointclass
point·class

This dictionary definitions page includes all the possible meanings, example usage and translations of the word pointclass.

Wiktionary

  1. pointclassnoun

    A collection of sets of points (ordinarily understood to be elements of some perfect Polish space), characterized by some sort of definability property.

Wikipedia

  1. Pointclass

    In the mathematical field of descriptive set theory, a pointclass is a collection of sets of points, where a point is ordinarily understood to be an element of some perfect Polish space. In practice, a pointclass is usually characterized by some sort of definability property; for example, the collection of all open sets in some fixed collection of Polish spaces is a pointclass. (An open set may be seen as in some sense definable because it cannot be a purely arbitrary collection of points; for any point in the set, all points sufficiently close to that point must also be in the set.) Pointclasses find application in formulating many important principles and theorems from set theory and real analysis. Strong set-theoretic principles may be stated in terms of the determinacy of various pointclasses, which in turn implies that sets in those pointclasses (or sometimes larger ones) have regularity properties such as Lebesgue measurability (and indeed universal measurability), the property of Baire, and the perfect set property.

Wikidata

  1. Pointclass

    In the mathematical field of descriptive set theory, a pointclass is a collection of sets of points, where a point is ordinarily understood to be an element of some perfect Polish space. In practice, a pointclass is usually characterized by some sort of definability property; for example, the collection of all open sets in some fixed collection of Polish spaces is a pointclass. Pointclasses find application in formulating many important principles and theorems from set theory and real analysis. Strong set-theoretic principles may be stated in terms of the determinacy of various pointclasses, which in turn implies that sets in those pointclasses have regularity properties such as Lebesgue measurability, the property of Baire, and the perfect set property.

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Numerology

  1. Chaldean Numerology

    The numerical value of pointclass in Chaldean Numerology is: 2

  2. Pythagorean Numerology

    The numerical value of pointclass in Pythagorean Numerology is: 2

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"pointclass." Definitions.net. STANDS4 LLC, 2024. Web. 28 Mar. 2024. <https://www.definitions.net/definition/pointclass>.

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