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A survey of some aspects of dynamical topology: Dynamical compactness and Slovak spaces

Dedicated to Professor Jürgen Scheurle on the occasion of his 65th birthday
Editors' note: Professor Sergiĭ Kolyada passed away on May 16, 2018. He will be missed by the mathematical community, as a mathematician and as a person. Due to his untimely death, Professor Kolyada could not implement the changes to the first version of the manuscript as suggested in the (positive) reviews. With the consent of Professor Kolyada's family, Professor L'ubomír Snoha (Matej Bel University, Banská Bystrica, Slovakia), a friend and colleague of Professor Kolyada, assumed the responsibility of carrying out the revision. The editors thank Professor Snoha for this invaluable contribution

This survey is based on lectures given by the author at the Max Planck Institute for Mathematics, Technical University of Munich, Paris-Sud University, Luminy Institute of Mathematics, Institute of Mathematics of Jussieu and several other mathematical departments in 2017

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