• Corpus ID: 50114238

# " Linearly Ordered and Generalized Ordered Spaces "

@inproceedings{RudinLO,
title={" Linearly Ordered and Generalized Ordered Spaces "},
author={Mary Ellen Rudin}
}
For any linearly ordered set (X, <), let I(<) be the topology on X that has the collection of all open intervals of (X, <) as a base. The topology I(<) is the open interval topology of the order < and (X, <, I(<)) is a linearly ordered topological space or LOTS. For a subset Y ⊆ X, it can happen that the relative topology I(<)| Y on Y does not coincide with the open interval topology I(< | Y) induced on Y by the restricted ordering. In some cases, there might be some other ordering of Y whose…
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