Hoyle, Hughes

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There are 17 item/s.

TitleDateViewsBrief Description
A Stieltjes integral existence theorem 1970 27 This paper is the result of inquiry into questions that arose concerning Stieltjes integrals....
An introduction to the game of hex 1970 25 Hex is a tree game (defined in chapter II) with several interesting properties. Hex never ends in a draw. Either White, the player who moves first, or Black, the other player, can force a win. If Black can force a win, then White can force a win. Thi...
Some banach algebras of analytic functions 1970 32 The purpose of the paper is to investigate the ideal structure in two Banach Algebras: A, the space of all complex-valued functions which are continuous on the closed unit disc U in the complex plane and analytic on the open unit disc U, and Hoo , th...
Bi-topological spaces 1971 102 Kelly initiated the study of bi-topological spaces in [3]. In this paper the concepts of pairwise-T, pairwise regular, pairwise Hausdorff, quasi-pseudo-metrizable, and quasi-metrizable are introduced, and the following theorem is proved. Theorem. If ...
Connected topologies for the unit interval 1971 17 The author has presented, with proofs, the solution of Hildebrand [2] to the problem proposed by Stallings [1] on the connectedness of the unit interval. It has been shown through Hildebrand's solution that Stallings" question has a negative answer, ...
Unusual separation axioms and topological spaces 1971 34 In this paper various types of separation axioms are studied. The ideas behind these results originated in [2], [4], and a seminar held by Dr. K. R. Gentry in the spring of 1969. In Chapters I and II, the separation axioms related to weakly equivalen...
Homeomorphic spaces in the plane 1971 173 The idea of topological equivalence, or homeomorphism, is one of the most basic in any study of topology. In this paper, pairs of spaces imbedded in the plane are compared to determine whether or not they are homeomorphic. The decisions are based on ...
Separation axioms weaker than T 1972 16 The purpose of this thesis is to briefly investigate ideas of Wilansky [2] on separation axioms between T1 and T2. In Chapter 1, preliminary definitions and theorems are stated and proved. In Chapter 2, a KC space, a US space, and a K space are defin...
Homeomorphic subspaces in the plane 1972 19 The idea of topological equivalence, or homeomorphic, is one of the basic considerations in any study of topology. Mrs. Yandell [3], in her master's thesis, compared pairs of spaces in the plane to determine whether or not they were homeomorphic. Dec...
Functions weaker than continuous functions 1972 19 Many properties which are characteristic of continuous function remain valid for several classes of non-continuous functions if appropriate limitations are imposed. Some problems of topology may be solved only through the study of non-continuous func...
Topological properties related to the upper bound topology 1972 12 If X is a set with topologies S and T, the upper bound topology for X is the set T[S,T] defined as follows: a set U c X is in T[S,T] provided if x € U there is an s € S and a t € T such that x € s n t c U. In this paper we examine the upper bound to...
Near-continuous functions and near-continuous homotopy 1972 30 The purpose of this thesis is to investigate and study the ideas of near-continuous functions and near-continuous homotopy. The ideas of near-continuous functions and near-continuous homotopy originated in [3] and [4]. The reader is expected to have ...
Aspects of numerical analysis relative to computing 1973 26 The purpose of this thesis is to investigate the problem of finding zeros of various functions through iterative methods. Chapter One is concerned with deriving an iterative function in such a manner as to insure that its fixed point is a zero of the...
Non-continuous set-valued functions 1973 50 In [1] the concept of continuous set-valued functions is defined and developed. Somewhat continuous functions are defined in [2]. The purpose of this thesis is to extend the concept of somewhat continuity to set-valued functions and prove or disprove...
Lattice isomorphisms 1974 22 The purpose of this thesis is to investigate the preservation of topological properties under lattice isomorphisms. The idea of using the usual lattice structure on topologies was originated by Birkhoff in [1], and has been studied by Thron in [2], [...
A compactness preserving topology for products sets 1975 14 The purpose of this thesis is to investigate the properties of certain topologies for a countable product of lattice isomorphic factor spaces. The idea of using lattice isomorphisms between factors to define a topology on a product space is due to Go...
Non-continuous fundamental groups of continuous loops 1976 13 Let (Y,T) be a topological space, let y0 ? Y, and let C(Y,y0) denote the set of continuous loops in Y at y0. It has long been known that using continuous functions as relating functions on C(Y,y0) produces an equivalence relation on C(Y,y0), and tha...