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This chapter is devoted to the classical theorem that says that if X is an irreducible continuum such that each of its indecomposable subcontinua has empty interior, then there exists a monotone mapping \(f:X\rightarrow [0,1]\) such that \(\operatorname {int}_{X}(f^{-1}(t)) =\emptyset \) for every \(t\in [0,1]\) .

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Irreducible Continua

  • 章节

  • 发表日期：

    2025年

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  • Alejandro Illanes

摘要

This chapter is devoted to the classical theorem that says that if X is an irreducible continuum such that each of its indecomposable subcontinua has empty interior, then there exists a monotone mapping \(f:X\rightarrow [0,1]\) such that \(\operatorname {int}_{X}(f^{-1}(t)) =\emptyset \) for every \(t\in [0,1]\) .