Concerning locally homotopy negligible sets and characterization of -manifolds
H. Toruńczyk (1978)
Fundamenta Mathematicae
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Concerning locally homotopy negligible sets and characterization of -manifolds
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We show the existence of a finite polyhedron P dominating infinitely many different homotopy types of finite polyhedra and such that there is a bound on the lengths of all strictly descending sequences of homotopy types dominated by P. This answers a question of K. Borsuk (1979) dealing with shape-theoretic notions of "capacity" and "depth" of compact metric spaces. Moreover, π₁(P) may be any given non-abelian poly-ℤ-group and dim P may be any given integer n ≥ 3.
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