Department of Mathematics Seminar Speaker: Simon Youl Affiliation: University of Auckland Title: A Subsequence Theorem for Generalised Inverse Limits Date: Tuesday, 22 Oct 2013 Time: 12pm Location: 303-412 The theory of inverse limits of inverse sequences whose bonding maps are singleton-valued and continuous is relatively well-understood. One central fact about inverse limits in this context is the so-called subsequence theorem, which ensures that the homeomorphism type of the inverse limit of an inverse sequence is not affected when we ”collapse” portions of the inverse sequence by function composition. Recently there has been some interest in so-called generalised inverse limits, which are inverse limits of inverse sequences whose bonding maps may be any upper semi-continuous set-valued maps. In this context, we do not have a general subsequence theorem, and the simple technique which is used to construct a homeomorphism between inverse limits in the proof of the earlier subsequence theorem fundamentally cannot be used. The question of which sets of conditions on the bonding maps would ensure that the subsequence theorem holds in the generalised context was raised by W.T. Ingram (2010). To this end, we introduce a different approach for constructing homeomorphisms between generalised inverse limits, and use it to prove a subsequence theorem for a particular situation involving generalised inverse limits. We also examine what partial converses to this generalised subsequence theorem can be obtained, especially in the simple case where each coordinate space is the arc. All welcome!
Posted on: Mon, 21 Oct 2013 20:51:29 +0000
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