Rings of Continuous Function

Charles E. Aull, Aull

• Publisher: CRC Press
• Year: 2020
• Print ISBN: 9781138441903
• eBook ISBN: 9781000154207
• Topic: Mathematics
• Subtopic: Functional Analysis
• Index: Mathematics

This book contains papers on algebra, functional analysis, and general topology, with a strong interaction with set theoretic axioms and involvement with category theory, presented in the special session on Rings of Continuous Functions held in 1982 in Cincinnati, Ohio.

N-Compactness, Metrizability, and Covering Dimension

Stanislaw Mrowka / Department of Mathematics, State University of New York at Buffalo, Buffalo, New York

1. INTRODUCTION

The paper contains author’s research revolving around P. Roy space Δ [1] and obtained between 1972–1978. In the first six sections the Roy method is applied to obtain N-compact spaces of positive dimension: the space μ and its metrizable subspaces μ₀ and μ₀₀(μ was reported on by the author at the Pittsburgh International Conference, December 1972, μ₀ and μ₀₀ were noticed around 1976–77). In addition, in sections 1 and 2 we give a description of a variant of Roy’s Δ, denoted here by V, its main purpose is to make the relation between Δ and μ more transparent. The last seven sections contain the proof that, under the continuum hypothesis, $\text{dim}{\text{μ}}_0^2=1$; more detailed comments on this topic as well as on the contributions of J. Teresawa are given in Sec. 8.

Numerical superscripts refer to notes at end.

On notations. Generally speaking, notations are explained in the text and they may change from section to section. The following convention how...

Table of contents

• Cover
• Half Title
• Pure and Applied Mathematics
• Lecture Notes
• Title Page
• Copyright Page
• Preface
• Table of Contents
• Contributors
• Some Genealogies in Rings of Continuous Functions
• A Cardinal Generalization of z-Embedding
• The Birth of the Stone-Čech Compactification
• Generalized Perfect Maps and a Theorem of I. Juhasz
• On Initially K-Compact Spaces
• Relatively Uniformly Complete Φ-Algebras
• Extreme Positive Operators and Function Spaces
• A Note on Extending Zero Sets from the Real Line
• Rings of Continuous Functions Are Rings: A Survey
• C(X) Has No Proper Functorial Hulls
• Algebraic Closures of Ꮂ-Groups of Continuous Functions
• Unsolved Problems on Algebraic Aspects of C(X)
• Prime Ideals in Function Rings
• Partial Extension of Bounded Functions to Compactifications
• The Extension of Uniformly Continuous Banach Space-Valued Mappings
• The Long Line as a Remainder
• N-Compactness, Metrizability, and Covering Dimension
• Concerning the Equation C({Пa}) = C(П{wXa})
• Some Topological Characterizations of the Generalized Continuum Hypothesis
• More Realcompact Spaces Scott
• Hausdorff Extension Properties: A Summary
• Problem Section
• Index