H-closed Extensions

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 7 in Extensions and Absolutes of Hausdorff Spaces, 1988, pp 531-611 from Springer

Abstract: Abstract In this chapter we begin a detailed investigation of the set H(X) of all H-closed extensions of a space X. We begin by considering strict and simple extensions of a space. We then construct and study the Fomin extension σX of an arbitrary space X, the Banaschewski-Fomin-Šanin extension μX of a semiregular space X, and one-point H-closed extensions of locally H-closed spaces. Next we consider the interrelationships among certain partitions of σX\X and the poset structure of H(X). We characterize and study those f ∈ C(X,Y) that can be extended to a function κf ∈ C(κX,κY). The chapter concludes with the study of Θ-equivalent H-closed extensions.

Date: 1988
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DOI: 10.1007/978-1-4612-3712-9_7

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