A Connected Topology for the Integers

DOI10.2307/2309340zbMath0202.33001OpenAlexW4249224158MaRDI QIDQ5599880

Solomon W. Golomb

Publication date: 1959

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2309340

Related Items (33)

A NOTE ON DENSITY AND THE DIRICHLET CONDITION ⋮ ARITHMETICALLY RELATED IDEAL TOPOLOGIES AND THE INFINITUDE OF PRIMES ⋮ Increasing sequence of topologies on the set of positive integers ⋮ Golomb's arithmetical semigroup topology and a semiprime sufficiency condition for Dirichlet's theorem ⋮ AN EXTENSION OF FURSTENBERG’S THEOREM OF THE INFINITUDE OF PRIMES ⋮ Properties of increasing sequence of Kirch-type topologies on the set of positive integers ⋮ Connections between connected topological spaces on the set of positive integers ⋮ On some relations between ideals of nowhere dense sets in topologies on positive integers ⋮ Unnamed Item ⋮ The Euclidean Criterion for Irreducibles ⋮ The Kirch space is topologically rigid ⋮ On some generalizations of the Kirch's ideal ⋮ The Golomb topology of polynomial rings, II ⋮ Increasing sequence of \(T_0\)-topologies on the set of positive integers ⋮ Aposyndesis in $\mathbb{N}$ ⋮ Generalizations of some ordinary and extreme connectedness properties of topological spaces to relator spaces ⋮ Coset topologies on \(\mathbb{Z}\) and arithmetic applications ⋮ Countable Connected Spaces ⋮ A note on Golomb topologies ⋮ Unnamed Item ⋮ Binary Relations in Mathematical Economics: On Continuity, Additivity and Monotonicity Postulates in Eilenberg, Villegas and DeGroot ⋮ On continuous self-maps and homeomorphisms of the Golomb space ⋮ The closures of arithmetic progressions in the common division topology on the set of positive integers ⋮ K‐analytic spaces with metrizable compacta ⋮ Ideals of nowhere dense sets in some topologies on positive integers ⋮ Topologically sensitive dynamical systems ⋮ The Golomb topology on a Dedekind domain and the group of units of its quotients ⋮ The Golomb Topology of Polynomial Rings ⋮ A universal coregular countable second-countable space ⋮ The closures of arithmetic progressions in Kirch's topology on the set of positive integers ⋮ The Darboux property for polynomials in Golomb’s and Kirch’s topologies ⋮ The connected countable spaces of Bing and Ritter are topologically homogeneous ⋮ The common division topology on $\mathbb{N}$

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