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- W2912663108 abstract "A Brown space is a topological space X such that for all non-empty open subsets U and V of X , we have cl cl . X X (U V ) ∩ ≠∅ ( ) It is clear that Brown spaces are connected and not completely Hausdorff. Given a b, , ∈ whose greatest common divisor is 1, we consider the arithmetic progression ( , ) = { : {0}}. P a b b an n G + ∈∪ The family G of all such arithmetic progressions is a base for a topology Gτ on . In this paper we show that for every d ∈ , the set (1, ) GP d is a Brown space which is dense in ( , ). G τ In particular, (, ) G τ is a Brown space. We also show that for each prime number p and every natural number c, such that the greatest common divisor between p and c is 1, the set (,) GP pc is totally separated. We write some consequences of such result. For example that the space (, ) G τ is not connected im kleinen at each of its points. This generalizes a result of Kirch AM.1 We also present a simpler proof of a result presented by Szczuka P.2 Some general properties of Brown spaces are also presented in this paper." @default.
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- W2912663108 date "2018-12-18" @default.
- W2912663108 modified "2023-10-01" @default.
- W2912663108 title "Brown spaces and the Golomb topology" @default.
- W2912663108 doi "https://doi.org/10.15406/oajmtp.2018.01.00042" @default.
- W2912663108 hasPublicationYear "2018" @default.
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