Print Email Facebook Twitter Stationary sets and on the existence of homeomorphisms between them Title Stationary sets and on the existence of homeomorphisms between them: Stationaire verzamelingen en het bestaan van homeomorphismes tussen deze Author Vermeulen, Joop (TU Delft Electrical Engineering, Mathematics and Computer Science) Contributor Hart, K.P. (mentor) Degree granting institution Delft University of Technology Programme Applied Mathematics Date 2020-08-31 Abstract Stationary sets are important tools in proofs of properties in sets of uncountable cardinality. In this thesis we look at mapping properties between stationary sets. First, the theory necessary for the construction and evaluation of stationary sets is made. That is the theory of ordinal, cardinal and regular cardinal numbers is build up from the level of knowledge of a mathematics student. Two important theorems for stationary sets, Fodor's theorem and the theorem of Ulam and Solovay, are proven. Next mapping properties of stationary subsets of a regular cardinal $\kappa$ under measurable functions is looked into. With these properties we construct a necessary condition for the existence of homeomorphisms between stationary sets; they may only differ on a non-stationary set. Lastly the amount of stationary subsets of a regular cardinal k without a homeomorphism between them is estimated as the cardinality of the power set of k. We find that there are 2 to the power k topologically incomparable subsets of k. Subject Stationary setRegular cardinalHomeomorphism To reference this document use: http://resolver.tudelft.nl/uuid:a68da48d-747b-4714-a5ad-75c1a802969f Part of collection Student theses Document type bachelor thesis Rights © 2020 Joop Vermeulen Files PDF BEP_8_.pdf 435.71 KB Close viewer /islandora/object/uuid:a68da48d-747b-4714-a5ad-75c1a802969f/datastream/OBJ/view