Monotone union property in a class M of separable metric spaces

Adeniran, Tinuoye M.

Displaying similar documents to “Monotone union property in a class M of separable metric spaces”

Separation axioms as absolute properties under monotone unions in weak topology

Adeniran, Tinuoye M. (1976)

Portugaliae mathematica

Similarity:

Schauder decomposition and best approximation in Banach Spaces

Jain, P.K., Ahmad, Khalil (1987)

Portugaliae mathematica

Similarity:

A Cantor set in the plane that is not σ-monotone

Aleš Nekvinda, Ondřej Zindulka (2011)

Fundamenta Mathematicae

Similarity:

A metric space (X,d) is monotone if there is a linear order < on X and a constant c such that d(x,y) ≤ cd(x,z) for all x < y < z in X, and σ-monotone if it is a countable union of monotone subspaces. A planar set homeomorphic to the Cantor set that is not σ-monotone is constructed and investigated. It follows that there is a metric on a Cantor set that is not σ-monotone. This answers a question raised by the second author.