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1. Slutskyy, Kostyantyn. Extending partial isomorphisms.

Degree: PhD, 0439, 2012, University of Illinois – Urbana-Champaign

There are two main topics in the thesis. In the second chapter we study two-dimensional classes of topological similarity in the groups of automorphisms of some linearly ordered Fraisse classes: the rationals, the linearly ordered random graph and the linearly ordered Urysohn space. The main theorem establishes meagerness of two-dimensional similarity classes in these groups. As a byproduct we get some results about the group of isometries of the Urysohn space. The third chapter is devoted to the metrics on the free products and HNN extensions of groups with two-sided invariant metrics. Using the approach of Graev to metrics on the free groups we show the existence of the coproducts in the category of groups with two-sided invariant metrics and Lipschitz homomorphisms. We then apply this theory to formulate a criterion when two topologically similar elements in a SIN Polish group are conjugate inside a bigger SIN Polish group. Advisors/Committee Members: Rosendal, Christian (advisor), van den Dries, Lou (Committee Chair), Solecki, Slawomir (committee member), Rosendal, Christian (committee member), Kapovitch, Ilia (committee member).

Subjects/Keywords: Polish groups; Graev metrics; topological similarity; induced conjugacy classes; Urysohn space

…variously attributed to V. A. Rokhlin and A. del Junco) that all the conjugacy classes in the… …n). The importance of diagonal conjugacy classes in the groups of automorphisms of… …e limit has comeager diagonal conjugacy classes. As topological similarity is an invariant… …for diagonal conjugacy, by showing that topological similarity classes are meager, one… …immediately deduces that also diagonal conjugacy classes are meager. As a concrete instance of this… 

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APA (6th Edition):

Slutskyy, K. (2012). Extending partial isomorphisms. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from

Chicago Manual of Style (16th Edition):

Slutskyy, Kostyantyn. “Extending partial isomorphisms.” 2012. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed April 02, 2020.

MLA Handbook (7th Edition):

Slutskyy, Kostyantyn. “Extending partial isomorphisms.” 2012. Web. 02 Apr 2020.


Slutskyy K. Extending partial isomorphisms. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2012. [cited 2020 Apr 02]. Available from:

Council of Science Editors:

Slutskyy K. Extending partial isomorphisms. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2012. Available from: