Atlas: Controlling disjointness with a hedgehog by Tomasz Kubiak

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Set Theory, Topology and Banach Spaces (Second International Topology Conference in Kielce)
July 7-11, 2008
Institute of Mathematics, Jan Kochanowski University in Kielce; co-organized by Technical University of Lodz
Kielce, Poland

Organizers
Taras Banakh, Piotr Koszmider, Wieslaw Kubis

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Controlling disjointness with a hedgehog
by
Tomasz Kubiak
Wydział Matematyki I Informatyki, Uniwersytet im. Adama Mickiewicza, Poznań, Poland
Coauthors: J. Gutierrez Garcia and M. A. de Prada Vicente

After Frantz's [Pacific J. Math. 169 (1995), 53-73] idea of controlling properties of extensions of continuous functions there has been an interest in extending families of continuous pairwise disjoint real-valued functions on normal spaces. We make the observation that disjoint extending a disjoint family of continuous functions is the same thing as extending a single continuous function with values in a hedgehog J(k) viewed as a bounded complete domain with its Lawson topology where k is the amount of pairwise disjoint functions which have to be extended. We provide a number of characterizations of spaces for which J(k) with its Lawson topology becomes an absolute extensor. In particular, this closes the circle of results related to disjoint extension theorems for normal spaces.

Date received: June 6, 2008