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- Nowhere_dense_set abstract "In mathematics, a nowhere dense set in a topological space is a set whose closure has empty interior. In a very loose sense, it is a set whose elements are not tightly clustered (as defined by the topology on the space) anywhere. The order of operations is important. For example, the set of rational numbers, as a subset of R, has the property that the interior has an empty closure, but it is not nowhere dense; in fact it is dense in R. Equivalently, a nowhere dense set is a set that is not dense in any nonempty open set.The surrounding space matters: a set A may be nowhere dense when considered as a subspace of a topological space X but not when considered as a subspace of another topological space Y. A nowhere dense set is always dense in itself.Every subset of a nowhere dense set is nowhere dense, and the union of finitely many nowhere dense sets is nowhere dense. That is, the nowhere dense sets form an ideal of sets, a suitable notion of negligible set. The union of countably many nowhere dense sets, however, need not be nowhere dense. (Thus, the nowhere dense sets need not form a sigma-ideal.) Instead, such a union is called a meagre set or a set of first category. The concept is important to formulate the Baire category theorem.".
- Nowhere_dense_set wikiPageExternalLink nowhere.htm.
- Nowhere_dense_set wikiPageID "48634".
- Nowhere_dense_set wikiPageLength "4468".
- Nowhere_dense_set wikiPageOutDegree "28".
- Nowhere_dense_set wikiPageRevisionID "704326956".
- Nowhere_dense_set wikiPageWikiLink Baire_category_theorem.
- Nowhere_dense_set wikiPageWikiLink Baire_space.
- Nowhere_dense_set wikiPageWikiLink Boundary_(topology).
- Nowhere_dense_set wikiPageWikiLink Cantor_set.
- Nowhere_dense_set wikiPageWikiLink Category:General_topology.
- Nowhere_dense_set wikiPageWikiLink Closed_set.
- Nowhere_dense_set wikiPageWikiLink Closure_(topology).
- Nowhere_dense_set wikiPageWikiLink Complement_(set_theory).
- Nowhere_dense_set wikiPageWikiLink Countable_set.
- Nowhere_dense_set wikiPageWikiLink Dense_set.
- Nowhere_dense_set wikiPageWikiLink Dyadic_rational.
- Nowhere_dense_set wikiPageWikiLink Finite_set.
- Nowhere_dense_set wikiPageWikiLink Ideal_(set_theory).
- Nowhere_dense_set wikiPageWikiLink Interior_(topology).
- Nowhere_dense_set wikiPageWikiLink Irreducible_fraction.
- Nowhere_dense_set wikiPageWikiLink Lebesgue_measure.
- Nowhere_dense_set wikiPageWikiLink Meagre_set.
- Nowhere_dense_set wikiPageWikiLink Negligible_set.
- Nowhere_dense_set wikiPageWikiLink Open_set.
- Nowhere_dense_set wikiPageWikiLink Rational_number.
- Nowhere_dense_set wikiPageWikiLink Sigma-ideal.
- Nowhere_dense_set wikiPageWikiLink Smith–Volterra–Cantor_set.
- Nowhere_dense_set wikiPageWikiLink Topological_space.
- Nowhere_dense_set wikiPageWikiLink Union_(set_theory).
- Nowhere_dense_set wikiPageWikiLink Unit_interval.
- Nowhere_dense_set wikiPageWikiLinkText "Nowhere dense set".
- Nowhere_dense_set wikiPageWikiLinkText "Nowhere dense".
- Nowhere_dense_set wikiPageWikiLinkText "nowhere dense set".
- Nowhere_dense_set wikiPageWikiLinkText "nowhere dense".
- Nowhere_dense_set wikiPageWikiLinkText "nowhere-dense".
- Nowhere_dense_set subject Category:General_topology.
- Nowhere_dense_set comment "In mathematics, a nowhere dense set in a topological space is a set whose closure has empty interior. In a very loose sense, it is a set whose elements are not tightly clustered (as defined by the topology on the space) anywhere. The order of operations is important. For example, the set of rational numbers, as a subset of R, has the property that the interior has an empty closure, but it is not nowhere dense; in fact it is dense in R.".
- Nowhere_dense_set label "Nowhere dense set".
- Nowhere_dense_set sameAs Q1991405.
- Nowhere_dense_set sameAs Řídká_množina.
- Nowhere_dense_set sameAs Denso_en_ninguna_parte.
- Nowhere_dense_set sameAs Ensemble_nulle_part_dense.
- Nowhere_dense_set sameAs קבוצה_דלילה.
- Nowhere_dense_set sameAs Insieme_mai_denso.
- Nowhere_dense_set sameAs 疎集合.
- Nowhere_dense_set sameAs 조밀한_곳이_없는_집합.
- Nowhere_dense_set sameAs Nergens_dichte_verzameling.
- Nowhere_dense_set sameAs Zbiór_nigdziegęsty.
- Nowhere_dense_set sameAs Conjunto_denso_em_lugar_nenhum.
- Nowhere_dense_set sameAs m.0c_s3.
- Nowhere_dense_set sameAs Нигде_не_плотное_множество.
- Nowhere_dense_set sameAs Ingenstans_tät_mängd.
- Nowhere_dense_set sameAs Ніде_не_щільна_множина.
- Nowhere_dense_set sameAs Q1991405.
- Nowhere_dense_set sameAs 无处稠密集.
- Nowhere_dense_set wasDerivedFrom Nowhere_dense_set?oldid=704326956.
- Nowhere_dense_set isPrimaryTopicOf Nowhere_dense_set.