Hausdorff Reductions of Leaves Spaces

Research output: Contribution to journalArticlepeer-review


Let F be a continuous mapping between topological spaces X and M and let x1 ∼ x2 if and only if these points belong to the same path connected component of F−1(F(x1)) be an equivalence relation on X. Under the assumption that the quotient mapping is open we construct a weaker equivalence ∧ on X and show that if we impose on F the lifting property, then the space X/∧ is Hausdorff. Replacing the lifting property with a stronger regularity property we show X/∧ is a manifold of the same class as M. Moreover, the construction of ∧ shows that X/∧ is the maximal manifold that can be obtained by weakening ∼. Finally we apply our results to holomorphic functions F on a complex manifold X.

Original languageEnglish (US)
Pages (from-to)567-580
Number of pages14
JournalAnalysis Mathematica
Issue number2
StatePublished - Jun 2022


  • fibering with singularities
  • quotient space

ASJC Scopus subject areas

  • Analysis
  • General Mathematics


Dive into the research topics of 'Hausdorff Reductions of Leaves Spaces'. Together they form a unique fingerprint.

Cite this