Skip to main content
MathOverflow

Return to Answer

Links
Source Link
LSpice
LSpice
  • 12.9k
  • 4
  • 45
  • 69

It is a theorem due to Blumberg (New Properties of All Real FunctionsNew Properties of All Real Functions -— Trans. AMS (1922)) and a topological space $X$ such that every real valued function admits a dense set on which it is continuous is sometimes called a Blumberg space.

Moreover, in Bredford & Goffman, Metric Spaces in which Blumberg's Theorem HoldsMetric Spaces in which Blumberg's Theorem Holds, Proc. AMS (1960) you can find a characterization of Blumberg spaces. Chapter 8 of the book Homeomorphisms in Analysis (mentioned by Gro-Tsen in the commentscomments, and available herehere) gives examples of Baire spaces which are not Blumberg spaces.

It is a theorem due to Blumberg (New Properties of All Real Functions - Trans. AMS (1922)) and a topological space $X$ such that every real valued function admits a dense set on which it is continuous is sometimes called a Blumberg space.

Moreover, in Bredford & Goffman, Metric Spaces in which Blumberg's Theorem Holds, Proc. AMS (1960) you can find a characterization of Blumberg spaces. Chapter 8 of the book Homeomorphisms in Analysis (mentioned by Gro-Tsen in the comments, and available here) gives examples of Baire spaces which are not Blumberg spaces.

It is a theorem due to Blumberg (New Properties of All Real Functions — Trans. AMS (1922)) and a topological space $X$ such that every real valued function admits a dense set on which it is continuous is sometimes called a Blumberg space.

Moreover, in Bredford & Goffman, Metric Spaces in which Blumberg's Theorem Holds, Proc. AMS (1960) you can find a characterization of Blumberg spaces. Chapter 8 of the book Homeomorphisms in Analysis (mentioned by Gro-Tsen in the comments, and available here) gives examples of Baire spaces which are not Blumberg spaces.

The answer previously claimed that Bedford & Goffman proved that a metric space is Blumberg iff it's a Baire space; but this is not what they proved, and that assertion is in fact false.
Source Link
Louigi Addario-Berry
Louigi Addario-Berry
  • 4.9k
  • 1
  • 29
  • 39

It is a theorem due to Blumberg (New Properties of All Real Functions - Trans. AMS (1922)) and a topological space $X$ such that every real valued function admits a dense set on which it is continuous is sometimes called a Blumberg space.

Moreover, in Bredford & Goffman, Metric Spaces in which Blumberg's Theorem Holds, Proc. AMS (1960) you can find the proof that a metric space ischaracterization of Blumberg iff it's aspaces. Chapter 8 of the book Homeomorphisms in Analysis (mentioned by Gro-Tsen in the comments, and available here) gives examples of Baire spacespaces which are not Blumberg spaces.

It is a theorem due to Blumberg (New Properties of All Real Functions - Trans. AMS (1922)) and a topological space $X$ such that every real valued function admits a dense set on which it is continuous is sometimes called a Blumberg space.

Moreover, in Bredford & Goffman, Metric Spaces in which Blumberg's Theorem Holds, Proc. AMS (1960) you can find the proof that a metric space is Blumberg iff it's a Baire space.

It is a theorem due to Blumberg (New Properties of All Real Functions - Trans. AMS (1922)) and a topological space $X$ such that every real valued function admits a dense set on which it is continuous is sometimes called a Blumberg space.

Moreover, in Bredford & Goffman, Metric Spaces in which Blumberg's Theorem Holds, Proc. AMS (1960) you can find a characterization of Blumberg spaces. Chapter 8 of the book Homeomorphisms in Analysis (mentioned by Gro-Tsen in the comments, and available here) gives examples of Baire spaces which are not Blumberg spaces.

Source Link
Samuele
Samuele
  • 1.2k
  • 9
  • 13

It is a theorem due to Blumberg (New Properties of All Real Functions - Trans. AMS (1922)) and a topological space $X$ such that every real valued function admits a dense set on which it is continuous is sometimes called a Blumberg space.

Moreover, in Bredford & Goffman, Metric Spaces in which Blumberg's Theorem Holds, Proc. AMS (1960) you can find the proof that a metric space is Blumberg iff it's a Baire space.