Concerning homotopy properties of compacta
Karol Borsuk (1968)
Fundamenta Mathematicae
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Karol Borsuk (1968)
Fundamenta Mathematicae
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Karol Borsuk (1970)
Fundamenta Mathematicae
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Karol Borsuk (1969)
Fundamenta Mathematicae
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Maria Moszyńska (1973)
Fundamenta Mathematicae
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Zvonko Čerin (1982)
Compositio Mathematica
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A. Suszycki (1983)
Fundamenta Mathematicae
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Sibe Mardešić, Jack Segal (1971)
Fundamenta Mathematicae
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Maria Moszyńska (1972)
Fundamenta Mathematicae
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Karol Borsuk (1970)
Fundamenta Mathematicae
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Danuta Kołodziejczyk (2007)
Fundamenta Mathematicae
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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...