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31 
The structure of βNRambally, Rodney Seunarine January 1970 (has links)
Our subject matter consists of a survey of the major results concerning the topological space βNN where N represents the space of natural numbers with the discrete topology, and βN the StoneČech compactification of N . We are mainly concerned with the results which were derived during the last ten years.
When there is no advantage in restricting our work to the space N we work with an arbitrary discrete space X and finally formulate our results in terms of βNN . In some cases, pre1960 results concerning βNN are obtained as special cases of the results we derive using an arbitrary discrete space X . The material presented is divided into four chapters.
In Chapter I, we discuss certain subsets of βNN which can be C*embedded in other subsets of βNN . This study leads to the conclusion that no proper dense subset of βNN can be C*embedded. In the second chapter we devise a general method of associating certain classes of points of βNN with certain subalgebras of C(N) . The Ppoints of βNN form one of these classes. The answer to R. S. Pierce's question, "Does there exist a point of βNN which lies simultaneously
in the closures of three pairwise disjoint open sets" is discussed in Chapter III. Finally in Chapter IV we present two proofs of the nonhomogeneity of βNN , without the use of the Continuum Hypothesis. / Science, Faculty of / Mathematics, Department of / Graduate

32 
Separation axioms and minimal topologiesLiaw, SawKer January 1971 (has links)
A hierarchy of separation axioms can be obtained by considering which axiom implies another. This thesis studies the properties of some separation axioms between T₀ and T₁ and investigates where each of the axioms belongs in this hierarchy. The behaviours of the axioms under strengthenings of topologies and cartesian products are considered.
Given a set X, the family of all topologies defined on X is a complete lattice. A study of topologies which are minimal in this lattice with respect to a certain separation axiom is made. We consider certain such minimal spaces, obtain some characterizations and study some of their properties. / Science, Faculty of / Mathematics, Department of / Graduate

33 
Orderable topological spacesGalik , Frank John January 1971 (has links)
Let (X , ਹ) be a topological space. If < is a total ordering on X , then (X , ਹ, <) is said to be an ordered topological space if a subbasis for ਹ is the collection of all sets of the form {x ∊ x  x < t} or [x ∊ x  t < x} where t ∊ X . The pair (X , ਹ) is said to be an orderable topological space if there exists a total ordering, < , on X such that (X , ਹ, <) is an ordered topological space.
Definition: Let T be a subspace of the real line ǀR . Let Q be the union of all nontrivial components of T , both of whose end points belong to C1ıʀ(C1ıʀ(T) T).
The following characterization of orderable subspaces of ǀR is due to M. E. Rudin.
Theorem: Let T be a subspace of ǀR with the relativized usual topology. Then T is orderable if and only if T satisfies the following two conditions:
(1) If T  Q is compact and (TQ) ก Clıʀ(Q) = Ø then either Q = Ø or T  Q = Ø
(2) If I is an open interval of ıʀ and p is an end point of I and if {p} U(I ก(TQ)) is compact and {p} =Clıʀ(IกQ)ก C1ıʀ(I ก(TQ)), then p ∉ T or {p} is a component of T.
This theorem enables us to prove a conjecture of I.L. Lynn, namely Corollary: if T contains no open compact sets then T is totally orderable.
If T is a subspace of an arbitrary ordered topological space a generalization of the theorem can be made. The generalized theorem is stated and some examples are given. / Science, Faculty of / Mathematics, Department of / Graduate

34 
A Set of Axioms for a Topological SpaceBatcha, Joseph Patrick 08 1900 (has links)
Axioms for a topological space are generally based on neighborhoods where "neighborhood" is an undefined term. Then, limit points are defined in terms of neighborhoods. However, limit points seem to be the basic concept of a topological space, rather than neighborhoods. For this reason, it will be attempted to state a set of axioms for a topological space, using limit point as the undefined concept, and to delete the idea of neighborhoods from the theory.

35 
Iterative solution of equations in linear topological spaces.Kotze, Wessel Johannes. January 1964 (has links)
No description available.

36 
NonArchimedian norms and boundsByers, Victor. January 1967 (has links)
No description available.

37 
Compact Convex Sets in Linear Topological SpacesRead, David R. 05 1900 (has links)
The purpose of this paper is to examine properties of convex sets in linear topological spaces with special emphasis on compact convex sets.

38 
Closed graph theorems for locally convex topological vector spacesHelmstedt, Janet Margaret 24 June 2015 (has links)
A Dissertation Submitted of the Faculty
of Science, University of the Witwatersrand,
Johannesburg in Partial Fulfilment
of the Requirements for the Degree of
Master of Science / Let 4 be the class of pairs of loc ..My onvex spaces (X,V) “h ‘ch
are such that every closed graph linear ,pp, 1 from X into V is
continuous. It B is any class of locally . ivex l.ausdortf spaces.
let & w . (X . (X.Y) e 4 for ,11 Y E B). " ‘his expository
dissertation, * (B) is investigated, firstly i r arbitrary B .
secondly when B is the class of C,complete paces and thirdly
whon B is a class of locally convex webbed s .ces

39 
Convex relations between topological vector spaces and adjoint convex processes.January 1989 (has links)
by Ma Mang Fai. / Thesis (M.Phil.)Chinese University of Hong Kong, 1989. / Bibliography: leaf 77.

40 
Integral representation for multiply superharmonic functions.Drinkwater, Anne Elizabeth January 1972 (has links)
No description available.

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