A new topology on the universal path space
Žiga Virk , Andreas Zastrow
AbstractWe generalize Brazas' topology on the fundamental group to the whole universal path space X, i.e., to the set of homotopy classes of all based paths. We develop basic properties of the new notion and provide a complete comparison of the obtained topology with the established topologies, in particular with the Lasso topology and the CO topology, i.e., the topology that is induced by the compact-open topology. It turns out that the new topology is the finest topology contained in the CO topology, for which the action of the fundamental group on the universal path space is a continuous group action.
|Other language title versions|
|Journal series||Topology and Its Applications, ISSN 0166-8641, (A 20 pkt)|
|Publication size in sheets||0.5|
|Keywords in English||topology on the fundamental group, topology on the path space, quasi topological fundamental group, compact open topology|
|Score|| = 20.0, ArticleFromJournal|
= 20.0, ArticleFromJournal
|Publication indicators||= 1; : 2017 = 1.051; : 2017 = 0.549 (2) - 2017=0.579 (5)|
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