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Remote point

Index Remote point

In general topology, a remote point is a point p that belongs to the Stone–Čech compactification \beta X of a Tychonoff space X but that does not belong to the topological closure within \beta X of any nowhere dense subset of X. Let \R be the real line with the standard topology. [1]

Table of Contents

  1. 20 relations: Bulletin of the American Mathematical Society, Closure (topology), Continuum hypothesis, General topology, Isolated point, Jeffrey H. Smith, Leonard Gillman, Metric space, Nathan Fine, Nowhere dense set, Number line, Pacific Journal of Mathematics, Point (geometry), Proceedings of the American Mathematical Society, Pseudocompact space, Separable space, Stone–Čech compactification, Topology and Its Applications, Tychonoff space, Zermelo–Fraenkel set theory.

Bulletin of the American Mathematical Society

The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.

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Closure (topology)

In topology, the closure of a subset of points in a topological space consists of all points in together with all limit points of. Remote point and closure (topology) are general topology.

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Continuum hypothesis

In mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets.

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General topology

In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.

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Isolated point

In mathematics, a point is called an isolated point of a subset (in a topological space) if is an element of and there exists a neighborhood of that does not contain any other points of. Remote point and isolated point are general topology.

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Jeffrey H. Smith

Jeffrey Henderson Smith is a former professor of mathematics at Purdue University in Lafayette, Indiana.

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Leonard Gillman

Leonard E. Gillman (January 8, 1917 – April 7, 2009) was an American mathematician, emeritus professor at the University of Texas at Austin.

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Metric space

In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points.

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Nathan Fine

Nathan Jacob Fine (22 October 1916 in Philadelphia – 18 November 1994 in Deerfield Beach, Florida) was an American mathematician who worked on basic hypergeometric series.

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Nowhere dense set

In mathematics, a subset of a topological space is called nowhere dense or rare if its closure has empty interior. Remote point and nowhere dense set are general topology.

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Number line

In elementary mathematics, a number line is a picture of a straight line that serves as spatial representation of numbers, usually graduated like a ruler with a particular origin point representing the number zero and evenly spaced marks in either direction representing integers, imagined to extend infinitely.

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Pacific Journal of Mathematics

The Pacific Journal of Mathematics is a mathematics research journal supported by several universities and research institutes, and currently published on their behalf by Mathematical Sciences Publishers, a non-profit academic publishing organisation, and the University of California, Berkeley.

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Point (geometry)

In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical spaces.

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Proceedings of the American Mathematical Society

Proceedings of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.

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Pseudocompact space

In mathematics, in the field of topology, a topological space is said to be pseudocompact if its image under any continuous function to R is bounded.

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Separable space

In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence. Remote point and separable space are general topology.

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Stone–Čech compactification

In the mathematical discipline of general topology, Stone–Čech compactification (or Čech–Stone compactification) is a technique for constructing a universal map from a topological space X to a compact Hausdorff space βX. Remote point and Stone–Čech compactification are general topology.

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Topology and Its Applications

Topology and Its Applications is a peer-reviewed mathematics journal publishing research on topology.

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Tychonoff space

In topology and related branches of mathematics, Tychonoff spaces and completely regular spaces are kinds of topological spaces.

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Zermelo–Fraenkel set theory

In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.

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References

[1] https://en.wikipedia.org/wiki/Remote_point