## Ordered compactifications and families of maps.(English)Zbl 0884.54019

Let $$X$$ be an ordered space. A subset $$\Phi$$ consisting of increasing, continuous functions from $$X$$ into $$[0,1]$$ is a defining family if it induces both the weak order and weak topology on $$X$$. For each such family the authors prove the existence of a smallest ordered compactification of $$X$$ with the property that each member of $$\Phi$$ can be extended over the compactification.

### MSC:

 54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)

### Keywords:

ordered space; ordered compactification; bicompletion
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