A new topology on the universal path space

Z. Virk, A. Zastrow, Topology and Its Applications 231 (2017) 186–196.

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Journal Article | Published | English
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Abstract
We 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.
Publishing Year
Date Published
2017-11-01
Journal Title
Topology and its Applications
Volume
231
Page
186 - 196
ISSN
IST-REx-ID

Cite this

Virk Z, Zastrow A. A new topology on the universal path space. Topology and its Applications. 2017;231:186-196. doi:10.1016/j.topol.2017.09.015
Virk, Z., & Zastrow, A. (2017). A new topology on the universal path space. Topology and Its Applications, 231, 186–196. https://doi.org/10.1016/j.topol.2017.09.015
Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” Topology and Its Applications 231 (2017): 186–96. https://doi.org/10.1016/j.topol.2017.09.015.
Z. Virk and A. Zastrow, “A new topology on the universal path space,” Topology and its Applications, vol. 231, pp. 186–196, 2017.
Virk Z, Zastrow A. 2017. A new topology on the universal path space. Topology and its Applications. 231, 186–196.
Virk, Ziga, and Andreas Zastrow. “A New Topology on the Universal Path Space.” Topology and Its Applications, vol. 231, Elsevier, 2017, pp. 186–96, doi:10.1016/j.topol.2017.09.015.

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