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Title: Compact topological spaces inspired by combinatorial constructions
Author: Al Mahrouqi, Sharifa
ISNI:       0000 0004 2745 191X
Awarding Body: University of East Anglia
Current Institution: University of East Anglia
Date of Award: 2013
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Due to Mrówka [24], polyadic spaces are compact Hausdorff spaces that are continuous images of some power of the one point compactification αλ of a discrete space λ. It turns out that many results about polyadic spaces hold for a more general class spaces, as we shall show in this thesis. For a sequence ‾λ = {λᵢ:iΕI} of cardinals, a compact Hausdorff space X is λ‾-multiadic if it is a continuous image of Πᵢ_ΕIαλᵢ. It is easy to observe that a λ‾-multiadic space is λ-polyadic, but whether the converse is true is a motivation of this dissertation. Although the individual polyadic and multiadic spaces differ, we show that the class of polyadic spaces is the same as multiadic class! Moreover, this dissertation is concerned with the combinatorics of multiadic class that can be used to give some of their topological structure. We give a Ramsey-like property for the class of multiadic compacta called Qλ where λ is a regular cardinal. For Boolean spaces this property is equivalent to the following: every uncountable collection of clopen sets contains an uncountable subcollection which is either linked or disjoint. We give generalizations of the Standard Sierpiński graph and use them to show that the property of being κ-multiadic is not inherited by regular closed sets for arbitrarily large κ.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available