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1997•Kyungpook mathematical journalRequires access

Using a Set to Construct a Group Topology

Ellen Clay, Bradd Clark, Victor Schneider

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Abstract

The usual topology on the real line can be constructed in a natural fashion from the set . It along with its opposite set and translates of these sets forms a subbasis for the usual topology. Hence the coarsets group topology on the reals containing the set is the usual topology. Many group topologies can be generated in this fashion. This paper will consider which group topologies can be generated in this fashion and which sets may be used to generate the topology.

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What this paper is about

The usual topology on the real line can be constructed in a natural fashion from the set . It along with its opposite set and translates of these sets forms a subbasis for the usual topology. Hence the coarsets group topology on the reals containing the set is the usual topology. Many group topologies can be generated in this fashion. This paper will consider which group topologies can be generated in this fashion and which sets may be used to generate the topology.

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Available abstract

The usual topology on the real line can be constructed in a natural fashion from the set . It along with its opposite set and translates of these sets forms a subbasis for the usual topology. Hence the coarsets group topology on the reals containing the set is the usual topology. Many group topologies can be generated in this fashion. This paper will consider which group topologies can be generated in this fashion and which sets may be used to generate the topology.

Key concepts: Comparison of topologies, Topology (electrical circuits), Initial topology, Extension topology, General topology, Network topology, Mathematics, Weak topology (polar topology)

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