Abstract
This chapter discusses problems in dimension theory, selections and continuum theory. All spaces are assumed to be metrizable and separable, if not stated otherwise. The group G denotes an Abelian group. K(G, n) is the Eilenberg–Mac Lane complex, that is, a CW complex such that πn(K(G, n)) ≈G and πi(K(G, n)) ≈ 0 for all i ≠n. The cohomological dimension of a space X with respect to the coefficient group G is denoted by dimG X. A space Y is an absolute (neighborhood) extensor for X [notation: Y ∈A(N)E(X)] if any map to Y, defined on an arbitrary closed subspace A of X, can be extended to a map of the whole X to Y (resp., to a map of some open neighborhood of A to Y). Section 2 of this chapter discusses the problems on extension dimension. In the third section, problems concerning selections and C-spaces are discussed. Section 4 discusses questions concerning the parametric version of disjoint disks property. The last section is devoted to locally connected Hausdorff continua and rim-metrizablity.
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