Displaying similar documents to “Concerning the sum of two continua each irreducible between the same pair of points”

The set functions 𝓣 and 𝒦 and irreducible continua

Leobardo Fernández, Sergio Macías (2010)

Colloquium Mathematicae

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We study the set functions 𝓣 and 𝒦 on irreducible continua. We present several properties of these functions when defined on irreducible continua. In particular, we characterize the class of irreducible continua for which these functions are continuous. We also characterize the class of 𝒦-symmetric irreducible continua.

Two-to-one continuous images of ℕ*

Alan Dow, Geta Techanie (2005)

Fundamenta Mathematicae

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A function is two-to-one if every point in the image has exactly two inverse points. We show that every two-to-one continuous image of ℕ* is homeomorphic to ℕ* when the continuum hypothesis is assumed. We also prove that there is no irreducible two-to-one continuous function whose domain is ℕ* under the same assumption.