Topologies on the real line

We prove that if a topology on the real line endows it with a topological group structure (additive) for which the interval ( 0 , + ∞ ) is an open set, so this topology is stronger than the usual topology. As a consequence we obtain characterizations of the usual topology as group topology and as ri...

Full description

Saved in:
Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2022-09, Vol.26 (4), Article 66
Main Authors: Mulero, M. A., Requejo, B.
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Econometrics
Fourier Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Potential Theory
Rings (mathematics)
Topology
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove that if a topology on the real line endows it with a topological group structure (additive) for which the interval ( 0 , + ∞ ) is an open set, so this topology is stronger than the usual topology. As a consequence we obtain characterizations of the usual topology as group topology and as ring topology. We also proved that if a topology on the real line is compatible with its usual lattice structure and is T 1 , so this topology is stronger than the usual topology, and as a consequence we obtain a characterization of the usual topology as lattice topology.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-022-00929-7