Compact complement topology

In mathematics, the compact complement topology is a topology defined on the set $\scriptstyle\mathbb{R}$ of real numbers, defined by declaring a subset $\scriptstyle X \subseteq \mathbb{R}$ open if and only if it is either empty or its complement $\scriptstyle\mathbb{R} \setminus X$ is compact in the standard Euclidean topology on $\scriptstyle\mathbb{R}$.

References

• Steen, Lynn Arthur; Seebach, J. Arthur Jr. (1995) [1978], Counterexamples in Topology (Dover reprint of 1978 ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-486-68735-3, MR507446 

This topology-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Topology Topology stubs Wikimedia Foundation. 2010. Игры ⚽ Нужна курсовая? Sweden in the Eurovision Song Contest 1963 Saint Justin Look at other dictionaries: Counterexamples in Topology —   Author(s) Lynn Arthur Steen J. Ar …   Wikipedia Topology — (Greek topos , place, and logos , study ) is the branch of mathematics that studies the properties of a space that are preserved under continuous deformations. Topology grew out of geometry, but unlike geometry, topology is not concerned with… …   Wikipedia Compact operator on Hilbert space — In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… …   Wikipedia Glossary of topology — This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also… …   Wikipedia Cocountable topology — The cocountable topology or countable complement topology on any set X consists of the empty set and all cocountable subsets of X, that is all sets whose complement in X is countable. It follows that the only closed subsets are X and the… …   Wikipedia Limit point compact — In mathematics, particularly topology, limit point compactness is a certain condition on a topological space which generalizes some features of compactness. In a metric space, limit point compactness, compactness, and sequential compactness are… …   Wikipedia Σ-compact space — In mathematics, a topological space is said to be sigma; compact if it is the union of countably many compact subspaces. A space is said to be sigma; locally compact if it is both sigma; compact and locally compact.Properties and Examples* Every… …   Wikipedia Fine topology (potential theory) — In mathematics, in the field of potential theory, the fine topology is a natural topology for setting the study of subharmonic functions. In the earliest studies of subharmonic functions, only smooth functions were considered, namely those for… …   Wikipedia Moore space (topology) — In mathematics, more specifically point set topology, a Moore space is a developable regular Hausdorff space. Equivalently, a topological space X is a Moore space if the following conditions hold: Any two distinct points can be separated by… …   Wikipedia List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”