# " 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…

## 8 Citations

Monotone extenders for bounded c-valued functions

- Mathematics
- 2010

Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, C∞(A, c) the set of all bounded continuous functions f : A→ c, and CA(X, c) the set of all functions f : X…

A glance into the anatomy of monotonic maps

- Mathematics
- 2019

Given an autohomeomorphism on an ordered topological space or its subspace, we show that it is sometimes possible to introduce a new topology-compatible order on that space so that the same map is…

When is $X\times Y$ homeomorphic to $X\times_l Y$?

- Mathematics
- 2018

We identify a class of linearly ordered topological spaces $X$ that may satisfy the property that $X\times X$ is homeomorphic to $X\times_l X$ or can be embedded into a linearly ordered space with…

When is X × Y homeomorphic to X ×l Y?

- MathematicsApplied General Topology
- 2019

We identify a class of linearly ordered topological spaces X that may satisfy the property that X × X is homeomorphic to X ×l X or can be embedded into a linearly ordered space with the stated…

In memory of my dear friend Alex Chigogidze ORDERING A SQUARE

- Mathematics
- 2015

We identify a condition on X that guarantees that any finite power of X is homeomorphic to a subspace of a linearly ordered space.

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