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The connectedness of arithmetic progressions in Furstenberg's, Golomb's, and Kirch's topologies

Szczuka P.

Demonstratio Mathematica

2010

Vol. 43, nr 4

899-909

In this paper we examine the connectedness of arithmetic progressions in the following topologies: Furstenberg's topology on the set of integers, Golomb's topology D on the set of positive integers, and Kirch's topology D′ on the set of positive integers. Immediate consequences of these studies are theorems concerning the connectedness and the locally connectedness of the topologies D and D′ proved by S. Golomb in 1959 and A. M. Kirch in 1969.