Journal of Mathematical Sciences: Advances and Applications
URYSOHN, AND 
AND INFINITELY MANY NEW CHARACTERIZATIONS
OF THE PROPERTYAuthor's: Charles Dorsett
Pages: [13] - [26]
Received Date: October 11, 2016
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121732
The (regular and 
) topological property, commonly denoted by
is a long studied, widely used separation
axiom. It is well-known that 
implies Urysohn, which implies 
which implies 
which implies 
and examples are known showing the
implications are not reversible. Thus questions concerning topological
properties for which the five separation axioms are equivalent arise.
In this paper, a new category of topological properties is introduced
and used to give infinitely many topological properties for which the
five separation axioms are equivalent, and results from the study of
weakly Po spaces and properties are used to give infinitely
many new characterizations of the separation axiom.
topological properties, weakly P properties, regular,
