S. Mardešić, On a problem concerning products in the category of shape, I. Banič: An Anderson-Choquet-type theorem and a characterization of weakly chainable continua
Topološki seminar Ljubljana-Maribor-Zagreb se bo sestal v soboto, 14.5.2015 v Ljubljani.
S. Mardešić, On a problem concerning products in the category of shape
In 1977 Y. Kodama proved that the Cartesian product of an FANR and a
paracompact space is a (direct) product in the shape category of
topological spaces Sh(Top). Since metrizable movable continua generalize
FANRs, it was natural to ask for products of such continua with other
spaces. In the present paper we show that the Cartesian product of a
metrizable movable continuum with a polyhedron need not be a product in
Sh(Top). A counterexample is the Cartesian product of the Hawaiian earring and the polyhedron that is the pointed sum of a sequence of
copies of circles.
Iztok Banič: An Anderson-Choquet-type theorem and a characterization of weakly chainable continua
We introduce the concept of proper convergence of a sequence of subspaces of a metric space and then prove that a continuum X is weakly chainable if there is a sequence of arcs converging properly to it. Also, we prove that a continuum X is weakly chainable if and only if there is a sequence of arcs in the Hilbert cube converging properly to an embedded copy of X. The proof is based on an Anderson-Choquet-type theorem (valid also for set-valued functions).
