Real Analysis Exchange

On Order Topologies and the Real Line

F. S. Cater

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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

Subjects
Primary: 26A03: Foundations: limits and generalizations, elementary topology of the line 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27} 54A05: Topological spaces and generalizations (closure spaces, etc.) 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30]

Keywords
real line order topology separable second countable

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.


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References

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