English

Open--constructible functions

General Topology 2014-01-14 v2

Abstract

We prove that if a continuous function f:Xf(X)f : X \to f(X) takes open sets into elements of the Boolean algebra generated by open and closed subsets in f(X)f(X), then there exist XnX,X_n \subset X, (nω)(n \in \omega) such that ff is open on every XnX_n and f(Xn)f(X_n) cover f(X). f(X).

Keywords

Cite

@article{arxiv.1302.1979,
  title  = {Open--constructible functions},
  author = {Alexey Ostrovsky},
  journal= {arXiv preprint arXiv:1302.1979},
  year   = {2014}
}
R2 v1 2026-06-21T23:23:05.514Z