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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 aren't tightly clustered close together (as defined by the topology on the space) anywhere at all. 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 "4494".
- Nowhere_dense_set wikiPageOutDegree "28".
- Nowhere_dense_set wikiPageRevisionID "683022969".
- 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.
- Nowhere_dense_set wikiPageWikiLink Countable_set.
- Nowhere_dense_set wikiPageWikiLink Dense_set.
- Nowhere_dense_set wikiPageWikiLink Dyadic_fraction.
- Nowhere_dense_set wikiPageWikiLink Dyadic_rational.
- Nowhere_dense_set wikiPageWikiLink Fat_Cantor_set.
- Nowhere_dense_set wikiPageWikiLink Finite_set.
- Nowhere_dense_set wikiPageWikiLink Ideal_(set_theory).
- Nowhere_dense_set wikiPageWikiLink Ideal_of_sets.
- Nowhere_dense_set wikiPageWikiLink Interior_(topology).
- Nowhere_dense_set wikiPageWikiLink Irreducible_fraction.
- Nowhere_dense_set wikiPageWikiLink Lebesgue_measure.
- Nowhere_dense_set wikiPageWikiLink Lowest_terms.
- 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 hasPhotoCollection Nowhere_dense_set.
- 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 aren't tightly clustered close together (as defined by the topology on the space) anywhere at all. 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 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 Q1991405.
- Nowhere_dense_set sameAs 无处稠密集.
- Nowhere_dense_set wasDerivedFrom Nowhere_dense_set?oldid=683022969.
- Nowhere_dense_set isPrimaryTopicOf Nowhere_dense_set.