Intrinsic Shape Property of Global Attractors in Metrizable Spaces
Received 30 October 2019; accepted 02 December 2019
2020, Vol. 16, no. 1, pp. 181-194
Author(s): Shekutkovski N., Shoptrajanov M.
This paper concerns the connection between shape theory and attractors for semidynamical
systems in metric spaces. We show that intrinsic shape theory from [6] is a convenient framework
to study the global properties which the attractor inherits from the phase space. Namely,
following [6] we’ll improve some of the previous results about the shape of global attractors in
arbitrary metrizable spaces by using the intrinsic approach to shape which combines continuity
up to a covering and the corresponding homotopies of first order.
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