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Displaying similar documents to “The set functions 𝓣 and 𝒦 and irreducible continua”

Absolute end points of irreducible continua

Janusz Jerzy Charatonik (1993)

Mathematica Bohemica

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A concept of an absolute end point introduced and studied by Ira Rosenholtz for arc-like continua is extended in the paper to be applied arbitrary irreducible continua. Some interrelations are studied between end points, absolute end points and points at which a given irreducible continuum is smooth.

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.

Concerning the sum of two continua each irreducible between the same pair of points

John Kline (1925)

Fundamenta Mathematicae

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The first part of the paper answers the question whether two different continua, each irreducible between the same pair of points could have a sum irreducible between two of its points. The second part shows certain properties of continua irreducible between the same pair of points and having the above mentioned property with respect to their sum.