The Paucity of Universal Spaces in Cohomological Dimension Theor
||Leonard R. Rubin, University of Oklahoma, Norman, USA
||The Paucity of Universal Spaces in Cohomological Dimension Theor
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 well-known 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 Stone-Cech compactiﬁcation is applied, how we make use of pseudo-compactness, and
how one might detect pseudo-compactness in a direct limit.
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