Dimension and extensions [EBook] / J.M. Aarts, T. Nishiura.
Dimension and extensions [EBook] / J.M. Aarts, T. Nishiura.
Two types of seemingly unrelated extension problems are discussed in this book. Their common focus is a longstanding problem of Johannes de Groot, the main conjecture of which was recently resolved. As is true of many important conjectures, a wide range of mathematical investigations had developed,...
Personal Name(s):  Aarts, Johannes Michael 

Nishiura, Togo  
Imprint: 
Amsterdam ; New York :
North Holland,
1993

Physical Description: 
1 online resource (xii, 331 p.) : ill. 
Note: 
englisch 
ISBN: 
9780444897404 0444897402 
Series Title: 
NorthHolland mathematical library ;
v. 48 
Subject (LOC):  
Full Text 
Two types of seemingly unrelated extension problems are discussed in this book. Their common focus is a longstanding problem of Johannes de Groot, the main conjecture of which was recently resolved. As is true of many important conjectures, a wide range of mathematical investigations had developed, which have been grouped into the two extension problems. The first concerns the extending of spaces, the second concerns extending the theory of dimension by replacing the empty space with other spaces. The problem of de Groot concerned compactifications of spaces by means of an adjunction of a set of minimal dimension. This minimal dimension was called the compactness deficiency of a space. Early success in 1942 lead de Groot to invent a generalization of the dimension function, called the compactness degree of a space, with the hope that this function would internally characterize the compactness deficiency which is a topological invariant of a space that is externally defined by means of compact extensions of a space. From this, the two extension problems were spawned. With the classical dimension theory as a model, the inductive, covering and basic aspects of the dimension functions are investigated in this volume, resulting in extensions of the sum, subspace and decomposition theorems and theorems about mappings into spheres. Presented are examples, counterexamples, open problems and solutions of the original and modified compactification problems. 