Matches in DBpedia 2015-10 for { ?s ?p "In mathematics, the particular point topology (or included point topology) is a topology where sets are considered open if they are empty or contain a particular, arbitrarily chosen, point of the topological space. Formally, let X be any set and p ∈ X. The collectionT = {S ⊆ X: p ∈ S or S = ∅}of subsets of X is then the particular point topology on X. There are a variety of cases which are individually named: If X = {0,1} we call X the Sierpiński space. This case is somewhat special and is handled separately. If X is finite (with at least 3 points) we call the topology on X the finite particular point topology. If X is countably infinite we call the topology on X the countable particular point topology. If X is uncountable we call the topology on X the uncountable particular point topology.A generalization of the particular point topology is the closed extension topology. In the case when X \ {p} has the discrete topology, the closed extension topology is the same as the particular point topology.This topology is used to provide interesting examples and counterexamples."@en }
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- Particular_point_topology abstract "In mathematics, the particular point topology (or included point topology) is a topology where sets are considered open if they are empty or contain a particular, arbitrarily chosen, point of the topological space. Formally, let X be any set and p ∈ X. The collectionT = {S ⊆ X: p ∈ S or S = ∅}of subsets of X is then the particular point topology on X. There are a variety of cases which are individually named: If X = {0,1} we call X the Sierpiński space. This case is somewhat special and is handled separately. If X is finite (with at least 3 points) we call the topology on X the finite particular point topology. If X is countably infinite we call the topology on X the countable particular point topology. If X is uncountable we call the topology on X the uncountable particular point topology.A generalization of the particular point topology is the closed extension topology. In the case when X \ {p} has the discrete topology, the closed extension topology is the same as the particular point topology.This topology is used to provide interesting examples and counterexamples.".