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2002β€’Proceedings of the American Mathematical SocietyOpen access

A continuum whose hyperspace of subcontinua is not 𝑔-contractible

Alejandro Illanes

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Abstract

A topological space Y Y is said to be g g -contractible provided that there exists a continuous onto function f : Y β†’ Y f:Y\rightarrow Y such that f f is homotopic to a constant function. Answering a question by Sam B. Nadler, Jr., in this paper we construct a metric continuum Z Z such that its hyperspace of subcontinua C ( Z ) C(Z) is not g g -contractible.

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A topological space Y Y is said to be g g -contractible provided that there exists a continuous onto function f : Y β†’ Y f:Y\rightarrow Y such that f f is homotopic to a constant function. Answering a question by Sam B. Nadler, Jr., in this paper we construct a metric continuum Z Z such that its hyperspace of subcontinua C ( Z ) C(Z) is not g g -contractible.

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Available abstract

A topological space Y Y is said to be g g -contractible provided that there exists a continuous onto function f : Y β†’ Y f:Y\rightarrow Y such that f f is homotopic to a constant function. Answering a question by Sam B. Nadler, Jr., in this paper we construct a metric continuum Z Z such that its hyperspace of subcontinua C ( Z ) C(Z) is not g g -contractible.

Key concepts: Contractible space, Hyperspace, Mathematics, Metric space, Pure mathematics, Constant (computer programming), Topological space, Combinatorics

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