author={David Lutzer},
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
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
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
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


Characterizations of Developable Topological Spaces
The class of developable topological spaces, which includes the metrizable spaces, has been fundamentally involved in investigations in point set topology. One example is the remarkable edifice of
Interval topology in subsets of totally orderable spaces
A topological space is said to be totally orderable if the points of the space can be totally ordered in such a way that the interval topology induced by this ordering coincides with the given
Concerning rings of continuous functions
The present paper deals with two distinct, though related, questions, concerning the ring C(X, R) of all continuous real-valued functions on a completely regular topological space X. The first of
On Metrizability of Topological Spaces
Our present work is divided into three sections. In §2 we study the metrizability of spaces with a G δ-diagonal (see Definition 2.1). In §3 we study the metrization of topological spaces by means of
Products of normal spaces with metric spaces
As is well known, the topological product of two normal spaces is not normal in general. Let X be a topological space. In 1951, C. H. DOWKEI~ [1] proved tha t the product space X × Y is normal for
A normal space X for which X×I is not normal
In [l ] C. Dowker gave a number of interesting characterizations of normal Hausdorff spaces whose cartesian product with the closed unit interval is not normal. Thus, such a space is often called a
A metrization theorem for linearly orderable spaces
A topological space X is linearly orderable if there is a linear ordering of the set X whose open interval topology coincides with the topology of X. It is known that if a linearly orderable space is
On stratifiable spaces
In the enclosed paper, it is shown that (a) the closed continuous image of a stratifiable space is stratifiable (b) the well-known extension theorem of Dugundji remains valid for stratifiable spaces
Countable paracompactness in linearly ordered spaces
A Hausdorff space X is said to be paracompact [2] provided that if W is a collection of open sets covering X, there exists a collection W' of open sets covering X such that (1) each element of W' is
A note on point-countability in linearly ordered spaces
In this note linearly ordered topological spaces (abbreviated LOTS) with a point-countable base are examined. It is shown that a LOTS is quasi-developable if and only if it has a a-point-finite base