Glasnik Matematicki, Vol. 40, No.2 (2005), 347-384.
A SUBSHAPE SPECTRUM FOR COMPACTA
Nikica Uglešić and Branko Červar
University of Split, Department of Mathematics,
21 000 Split, Teslina 12/III, Croatia
Abstract. A sequence of categories and functors between them are
constructed. They form a subshape spectrum for compacta in
the following sense: Each of these categories classifies compact
ANR's just as the homotopy category does; the classification of
compacta by the "finest" of these categories coincides with the
shape type classification; moreover, the finest category contains
a subcategory which is isomorphic to the shape category; there
exists a functor of the shape category to each of these
categories, as well as of a "finer" category to a
"coarser" one; the functors commute
according to the indices.
Further, a few applications of the "subshape spectrum theory" are demonstrated.
It is shown that the S*-equivalence (a uniformization of the Mardešić
S-equivalence) and the q*-equivalence (a uniformization
of the Borsuk quasi-equivalence) admit the category
characterizations within the subshape spectrum, and that the
q*-equivalence implies (but is not equivalent to) the
2000 Mathematics Subject Classification.
Key words and phrases. Compactum, ANR, inverse sequence, limit, shape type,
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