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-Ultrametric Spaces and Presheaves by Nathanael Leedom Ackerman
 

Summary: -Ultrametric Spaces and Presheaves
by Nathanael Leedom Ackerman
Abstract
In this paper we will explore the relationship between -Ultrametric
Spaces and Separated Presheaves. We will then use this relationship
to prove some new results about Separated Presheaves with nice prop-
erties.
-Ultrametric spaces (as in this paper) have been extensively studied (see for
example [7], [8], [1]) as a way to weaken the notion of an ultrametric space
while still providing enough structure to be useful. -Ultrametric spaces are
spaces which satisfy all the axioms of an ultrametric space except that the
distance function takes values in a fixed complete lattice (and not necessarily
in the reals) 1
We begin this paper in Section 1 by reviewing the relevant definitions
before discussing in Section 2 the close connection between the categories of
-Ultrametric Spaces and the category of separated presheaves on op
.
In Section 3, we will show how all categories with epi-monic factoriza-
tions can be viewed as having Hom-sets which are -Ultrametric spaces. This
will then allow us, in Section 4, to translate results about Generalized Ul-

  

Source: Ackerman, Nate - Department of Mathematics, University of Pennsylvania

 

Collections: Mathematics