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The Paucity of Universal Spaces in Cohomological Dimension Theor
Vrijeme: 
19.5.2010 17:00 
Predavaonica: 
005 
Predavač: 
Leonard R. Rubin, University of Oklahoma, Norman, USA 
Naziv: 
The Paucity of Universal Spaces in Cohomological Dimension Theor 
Opis:
Abstract. Let C be a class of spaces. An element Z ∈ C is called universal for C
if each element of C embeds topologically in Z. It is wellknown that for each n ∈ N,
there exists a universal element for the class of metrizable compacta X of (covering)
dimension dim X ≤ n. We are going to speak about the question of whether such universal
compacta exist for other dimension theories, in particular for cohomological dimension over
an abelian group G, dim_G , which is a type of dimension theory with many parallels to
that of covering dimension.
It will be our goal to describe some of the techniques we use to prove that such universal
compacta do not exist in general for dim_G . An important method will be that of direct
systems, direct limits, and induced maps of such systems and their limits. We will discuss
how StoneCech compactiﬁcation is applied, how we make use of pseudocompactness, and
how one might detect pseudocompactness in a direct limit.

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