Extensions of Spaces

Jack R. Porter and R. Grant Woods
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Jack R. Porter: The University of Kansas, Department of Mathematics
R. Grant Woods: University of Manitoba, Department of Mathematics

Chapter Chapter 4 in Extensions and Absolutes of Hausdorff Spaces, 1988, pp 238-361 from Springer

Abstract: Abstract The reader may recall that a space Y is called an extension of a space X if X is a dense subspace of Y. One of the reasons for studying extensions is the possibility of shifting a problem concerning a space X to a problem concerning an extension Y of X where Y is a “nicer” space than X and the “shifted” problem can be solved. Thus, an important goal in extension theory is to generate “nice” extensions of a fixed space X. After we have defined and developed some of the basic notions of extension theory, we will proceed to generate all the compact extensions of a Tychonoff space and all the compact, zero-dimensional extensions of a zero-dimensional space. In the final section of the chapter, we study certain “nice” extensions of an arbitrary (Hausdorff) space, namely the H-closed extensions.

Keywords: Open Neighborhood; Maximal Ideal; Compact Space; Open Filter; Stone Space (search for similar items in EconPapers)
Date: 1988
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DOI: 10.1007/978-1-4612-3712-9_4

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