# ORDERED TOPOLOGICAL SPACES

@inproceedings{Lutzer1980ORDEREDTS,
title={ORDERED TOPOLOGICAL SPACES},
author={David Lutzer},
year={1980}
}
On the Orderability Problem and the Interval Topology
The class of LOTS (linearly ordered topological spaces, i.e. spaces equipped with a topology generated by a linear order) contains many important spaces, like the set of real numbers, the set of
A Step Beyond Topology
ABSTRACT: The questions which motivated the development of neighborhood (nbhd) lattices as a generalization of topological (top) spaces are discussed. Nbhd systems, which are shown to be appropriate
-DIAGONALS AND WEAK -SPACES IN GO-SPACES
• Mathematics
• 2010
1. Definitions and Preliminaries In [5], topological spaces with various types of diagonals and weak $\sigma$ -spaces are studied. In this paper these notions are extended and reflected upon
9-1-1987 Ordered Products of Topological Groups
1. Introduction The topology most often used on a totally ordered group (G, <) is the interval topology. There are usually many ways to totally order GxG (e.g., the lexicographic order) but the
Perfect images of generalized ordered spaces
• Mathematics
• 2018
We study the class of perfect images of generalized ordered (GO) spaces, which we denote by PIGO. Mary Ellen Rudin’s celebrated result characterizing compact monotonically normal spaces as the
Problems in perfect ordered spaces
• Mathematics
• 1990
In his landmark paper " Mappings and Spaces " [1966] A. V. Arkhangel-ski˘ ı introduced the class MOBI (Metric Open Bicompact Images) as the intersection of all classes of topological spaces
A glance into the anatomy of monotonic maps
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

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