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H-closed Extensions

In: Extensions and Absolutes of Hausdorff Spaces

Author

Listed:
  • Jack R. Porter

    (The University of Kansas, Department of Mathematics)

  • R. Grant Woods

    (University of Manitoba, Department of Mathematics)

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.

Suggested Citation

  • Jack R. Porter & R. Grant Woods, 1988. "H-closed Extensions," Springer Books, in: Extensions and Absolutes of Hausdorff Spaces, chapter 0, pages 531-611, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3712-9_7
    DOI: 10.1007/978-1-4612-3712-9_7
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