On the Whitehead theorem in shape theory I
Sibe Mardešić (1976)
Fundamenta Mathematicae
Similarity:
Sibe Mardešić (1976)
Fundamenta Mathematicae
Similarity:
Sławomir Nowak (1985)
Fundamenta Mathematicae
Similarity:
Sibe Mardešić, Jack Segal (1971)
Fundamenta Mathematicae
Similarity:
Thomas Sanders (1981)
Fundamenta Mathematicae
Similarity:
Vo-Thanh Liem (1985)
Fundamenta Mathematicae
Similarity:
James Draper, James Keesling (1976)
Fundamenta Mathematicae
Similarity:
A. Suszycki (1983)
Fundamenta Mathematicae
Similarity:
Karol Borsuk (1961)
Fundamenta Mathematicae
Similarity:
Danuta Kołodziejczyk (2007)
Fundamenta Mathematicae
Similarity:
The notions of capacity and depth of compacta were introduced by K. Borsuk in the seventies together with some open questions. In a previous paper, in connection with one of them, we proved that there exist polyhedra with polycyclic fundamental groups and infinite capacity, i.e. dominating infinitely many different homotopy types (or equivalently, shapes). In this paper we show that every polyhedron with virtually polycyclic fundamental group has finite depth, i.e., there is a bound...
Danuta Kołodziejczyk (2003)
Fundamenta Mathematicae
Similarity:
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.
Sławomir Nowak (1979)
Fundamenta Mathematicae
Similarity: