Some quantitative properties of shapes

Karol Borsuk

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On a metrization of the hyperspace of a metric space

Karol Borsuk (1977)

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Concerning the ordering of shapes of compacta

Karol Borsuk, W. Holsztyński (1970)

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Three questions of Borsuk concerning movability and fundamental retraction

C. Cox (1973)

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Stanisław Godlewski (1981)

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Karol Borsuk (1969)

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Quasi-equivalence of compacta and spaces of components.

José M. Rodríguez Sanjurjo (1980)

Collectanea Mathematica

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Let X, Y be two compacta with Sh(X) = Sh (Y). Then, the spaces of components of X, Y are homeomorphic. This does not happen, in general, when X, Y are quasi-equivalent. In this paper we give a sufficient condition for the existence of a homeomorphism between the spaces of components of two quasi-equivalent compacta X, Y which maps each component in a quasi-equivalent component.