## Real Analysis Exchange

### On Order Topologies and the Real Line

F. S. Cater

#### Abstract

We find order topologies that are universal for certain topological properties. An order topology $T$ enjoys a given property if and only if there is an order preserving homeomorphism of $T$ into the universal space for this property. We give similar results for order preserving mappings in place of homeomorphisms.

#### Article information

Source
Real Anal. Exchange Volume 25, Number 2 (1999), 771-780.

Dates
First available: 3 January 2009

Permanent link to this document
http://projecteuclid.org/euclid.rae/1230995411

Mathematical Reviews number (MathSciNet)
MR1778529

Zentralblatt MATH identifier
1014.54020

#### Citation

Cater, F. S. On Order Topologies and the Real Line. Real Analysis Exchange 25 (1999), no. 2, 771--780. http://projecteuclid.org/euclid.rae/1230995411.

#### References

• J. Kelley, General topology, van Nostrand, New York, 1955.
• W. Sierpinski, General topology, The University of Toronto Press, 1934.