Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Open_set> ?p ?o }
- Open_set abstract "In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line. The simplest example is in metric spaces, where open sets can be defined as those sets which contain an open ball around each of their points (or, equivalently, a set is open if it doesn't contain any of its boundary points); however, an open set, in general, can be very abstract: any collection of sets can be called open, as long as the union of an arbitrary number of open sets is open, the intersection of a finite number of open sets is open, and the space itself is open. These conditions are very loose, and they allow enormous flexibility in the choice of open sets. In the two extremes, every set can be open (called the discrete topology), or no set can be open but the space itself (the indiscrete topology).In practice, however, open sets are usually chosen to be similar to the open intervals of the real line. The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined. Once a choice of open sets is made, the properties of continuity, connectedness, and compactness, which use notions of nearness, can be defined using these open sets.Each choice of open sets for a space is called a topology. Although open sets and the topologies that they comprise are of central importance in point-set topology, they are also used as an organizational tool in other important branches of mathematics. Examples of topologies include the Zariski topology in algebraic geometry that reflects the algebraic nature of varieties, and the topology on a differential manifold in differential topology where each point within the space is contained in an open set that is homeomorphic to an open ball in a finite-dimensional Euclidean space.".
- Open_set thumbnail Red_blue_circle.svg?width=300.
- Open_set wikiPageID "39358".
- Open_set wikiPageLength "14779".
- Open_set wikiPageOutDegree "63".
- Open_set wikiPageRevisionID "702792436".
- Open_set wikiPageWikiLink Abuse_of_notation.
- Open_set wikiPageWikiLink Algebraic_geometry.
- Open_set wikiPageWikiLink Algebraic_variety.
- Open_set wikiPageWikiLink Ball_(mathematics).
- Open_set wikiPageWikiLink Boundary_(topology).
- Open_set wikiPageWikiLink Category:General_topology.
- Open_set wikiPageWikiLink Clopen_set.
- Open_set wikiPageWikiLink Closed_set.
- Open_set wikiPageWikiLink Compact_space.
- Open_set wikiPageWikiLink Connectedness.
- Open_set wikiPageWikiLink Continuous_function.
- Open_set wikiPageWikiLink Countable_set.
- Open_set wikiPageWikiLink Differentiable_manifold.
- Open_set wikiPageWikiLink Differential_topology.
- Open_set wikiPageWikiLink Discrete_space.
- Open_set wikiPageWikiLink Empty_set.
- Open_set wikiPageWikiLink Euclidean_distance.
- Open_set wikiPageWikiLink Euclidean_space.
- Open_set wikiPageWikiLink Euclidean_topology.
- Open_set wikiPageWikiLink Existential_quantification.
- Open_set wikiPageWikiLink Function_(mathematics).
- Open_set wikiPageWikiLink General_topology.
- Open_set wikiPageWikiLink Gδ_set.
- Open_set wikiPageWikiLink Image_(mathematics).
- Open_set wikiPageWikiLink Interior_(topology).
- Open_set wikiPageWikiLink Intersection_(set_theory).
- Open_set wikiPageWikiLink Interval_(mathematics).
- Open_set wikiPageWikiLink Metric_(mathematics).
- Open_set wikiPageWikiLink Metric_space.
- Open_set wikiPageWikiLink Neighbourhood_(mathematics).
- Open_set wikiPageWikiLink Open_and_closed_maps.
- Open_set wikiPageWikiLink Rational_number.
- Open_set wikiPageWikiLink Real_line.
- Open_set wikiPageWikiLink Real_number.
- Open_set wikiPageWikiLink Set_(mathematics).
- Open_set wikiPageWikiLink Subset.
- Open_set wikiPageWikiLink Topological_indistinguishability.
- Open_set wikiPageWikiLink Topological_space.
- Open_set wikiPageWikiLink Topology.
- Open_set wikiPageWikiLink Trivial_topology.
- Open_set wikiPageWikiLink Uniform_space.
- Open_set wikiPageWikiLink Union_(set_theory).
- Open_set wikiPageWikiLink Universal_quantification.
- Open_set wikiPageWikiLink Zariski_topology.
- Open_set wikiPageWikiLink File:Red_blue_circle.svg.
- Open_set wikiPageWikiLinkText "Open set".
- Open_set wikiPageWikiLinkText "Open_set".
- Open_set wikiPageWikiLinkText "domain".
- Open_set wikiPageWikiLinkText "neighbourhood".
- Open_set wikiPageWikiLinkText "open discs".
- Open_set wikiPageWikiLinkText "open domain".
- Open_set wikiPageWikiLinkText "open neighborhood".
- Open_set wikiPageWikiLinkText "open neighbourhood".
- Open_set wikiPageWikiLinkText "open region".
- Open_set wikiPageWikiLinkText "open set".
- Open_set wikiPageWikiLinkText "open subset".
- Open_set wikiPageWikiLinkText "open subsets".
- Open_set wikiPageWikiLinkText "open".
- Open_set wikiPageWikiLinkText "openness".
- Open_set id "2925".
- Open_set id "p/o068310".
- Open_set title "Open Set".
- Open_set title "Open set".
- Open_set wikiPageUsesTemplate Template:PlanetMath_reference.
- Open_set wikiPageUsesTemplate Template:Refimprove.
- Open_set wikiPageUsesTemplate Template:Reflist.
- Open_set wikiPageUsesTemplate Template:Springer.
- Open_set wikiPageUsesTemplate Template:Topology.
- Open_set subject Category:General_topology.
- Open_set hypernym Concept.
- Open_set type Redirect.
- Open_set comment "In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.".
- Open_set label "Open set".
- Open_set sameAs Q213363.
- Open_set sameAs مجموعة_مفتوحة.
- Open_set sameAs Отворено_множество.
- Open_set sameAs Conjunt_obert.
- Open_set sameAs Otevřená_množina.
- Open_set sameAs Åben_mængde.
- Open_set sameAs Offene_Menge.
- Open_set sameAs Malfermita_aro.
- Open_set sameAs Conjunto_abierto.
- Open_set sameAs Lahtine_hulk.
- Open_set sameAs مجموعه_باز.
- Open_set sameAs Avoin_joukko.
- Open_set sameAs Ouvert_(topologie).
- Open_set sameAs קבוצה_פתוחה.
- Open_set sameAs Nyílt_halmaz.
- Open_set sameAs Himpunan_terbuka.
- Open_set sameAs Opið_mengi.
- Open_set sameAs Insieme_aperto.
- Open_set sameAs 開集合.
- Open_set sameAs 열린_집합.
- Open_set sameAs Ачык_көптүк.