Burke, Maxim R. “Continuous Functions Which Take a Somewhere Dense Set of Values on Every Open Set”. Topology and Its Applications, vol. 103, no. 1, 2000, pp. 95-110, https://doi.org/10.1016/S0166-8641(98)00163-1.

Genre

  • Journal Article
Contributors
Author: Burke, Maxim R.
Date Issued
2000
Abstract

We study the class of Tychonoff spaces that can be mapped continuously into R in such a way that the preimage of every nowhere dense set is nowhere dense. We show that every metric space without isolated points is in this class. We also give examples of spaces which have nowhere constant continuous maps into R and are not in this class. (C) 2000 Elsevier Science B.V. All rights reserved.

Note

Univ Prince Edward Isl, Dept Math & Comp Sci, Charlottetown, PE C1A 4P3, Canada. Univ Toronto, Dept Math, Toronto, ON M5S 1A1, Canada.; Burke, MR, Univ Prince Edward Isl, Dept Math & Comp Sci, Charlottetown, PE C1A 4P3, Canada.

AMSTERDAM; PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS

ELSEVIER SCIENCE BV

Source type: Electronic(1)

Language

  • English

Subjects

  • nowhere constant
  • continuous function
  • Mathematics, Applied
  • set of range uniqueness
  • Mathematics
  • nowhere thin
Page range
95-110
Host Title
Topology and its Applications
Host Abbreviated Title
Topology Appl.
Volume
103
Issue
1
ISSN
0166-8641
DOI
https://doi.org/10.1016/S0166-8641(98)00163-1

Department