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Abstract
USING THE CONCEPT OF IDEALS
This thesis, which consists of four chapters, is devoted to give further study of operators
w.r.t. proximity relations 0 and ideals I on a non empty set X.
In the introductory chapter I, we recall most of the definitions, preliminaries and
conventions to be used throughout this thesis.
In chapter II, we introduce and study the local function operator ( ). and the com-
patibility relation of 0 with I. We study the relation between the Smirnov compactification
of an Ef-proximity and the characterization of the generated Lo-proximity induced by the
original proximity and the ideal I, of finite subsets. Since the concept of proximally con-
tinuous mapping plays an important role in proximity spaces, we introduce and study the
concept of *-proximally continuous mapping (in the class of proximity spaces induced by
old ones with an ideal).
In chapter III, we introduce and study a finer proximity relation I from a given
proximity relation 0 and an ideal I on set X.
The purpose of chapter IV, is to study the principal concept in our work, namely
the *-operator w.r.t. a syntopogenous order and an ideal.