Vol. 105, No. 2, 1983

Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Sup-characterization of stratifiable spaces

Carlos R. Borges and Gary Fred Gruenhage

Vol. 105 (1983), No. 2, 279–284
Abstract

We prove that a T1-space (X,τ) is stratifiable if and only if, for each U τ, one can find a continuous function fU : X I such that fU1(0) = X U and, for each 𝒰 ⊂ τ, supU∈𝒰fU is continuous. This result is closely related to characterizations of metrizable and paracompact spaces, by J. Nagata, and J. Guthrie and M. Henry.

Mathematical Subject Classification 2000
Primary: 54E20
Milestones
Received: 19 August 1981
Published: 1 April 1983
Authors
Carlos R. Borges
Gary Fred Gruenhage