文档介绍：IJMMS 2003:2, 109–117
PII. S0161171203007646
http://ijmms.
© Hindawi Publishing Corp.
PACTNESS IN APPROACH SPACES II
R. LOWEN and C. VERBEECK
Received 20 May 2001
This paper studies the stability properties of the concepts of pactness
introduced by the authors in 1998. We show that all of these concepts are stable
for contractive, expansive images and for products.
2000 Mathematics Subject Classification: 54A05, 54B10, 54D45.
1. Introduction. Having introduced notions of pactness, basis lo-
pactness and related measures, and having studied the basic relation-
ship among these concepts in [3], in this paper we study stability properties.
Keeping in mind the stability properties of pactness in TOP, the cat-
egory of topological spaces and continuous maps, we study how our notions
behave under mappings and products. Especially, in the topological case, the
maps which are required in order to preserve pactness are continuous
open surjections. This necessitated first finding out what is the right notion of
open map in AP. This is duly done in this paper, and it turns out that the notion
which we use has nice characterizations for a number of primitive approach
structures. Of course, it also turns out to be the right concept in connection
with pactness.
2. Properties of pactness in AP. In the construct of topological
spaces, we have the following prop