End-Extension of Ordered Set/Examples/Closed Real Interval

Example of End-Extension of Ordered Set

The closed real interval $\closedint 0 1$ is:

an end-extension of the half-open interval $\hointr 0 1$
but not an end-extension of the open interval $\openint 0 1$.


Sources

  • 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations
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