This article is cited in 10 papers

Complemented topologies on abelian groups

E. G. Zelenyuk^a, I. V. Protasov<sup>b

a</sup> Institute for Applied Problems of Mechanics and Mathematics, NAS Ukraine
^b National Taras Shevchenko University of Kyiv

Abstract: A topology $\tau$ on a group $G$ is complemented if there exists an indiscrete topology $\tau'$ on $G$ such that $U\cap V=\{0\}$ for suitable neighborhoods of zero $U$ and $V$ in the topologies $\tau$ and $\tau'$. The authors give a complementation test for an arbitrary topology. Locally compact groups with complemented topologies have been described. A group all of whose continuous homomorphic images are complete is proved to be compact. A family of $2^\omega$ topologies that are pairwise complementary to one another is defined for an arbitrary group.

UDC: 512.546

Received: 27.03.1999

 English version: Siberian Mathematical Journal, 2001, 42:3, 465–372

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