Extremally Disconnected Spaces and Absolutes

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 6 in Extensions and Absolutes of Hausdorff Spaces, 1988, pp 440-530 from Springer

Abstract: Abstract One of the best behaved classes of functions encountered in general topology is the class of perfect functions, which was discussed in 1.8. As we have already seen, two topological spaces, one of which is the perfect continuous image of the other, will have many topological properties in common. (Examples of a number of such properties are given in 1J.) Perfect continuous surjections also play an important role in compactification theory (see 4.2(f,g) and in the study of extension properties (see 5.9(c)). Roughly speaking, if you cannot construct a homeomorphism between X and Y, constructing a perfect continuous surjection between them is the next best goal.

Keywords: Open Subset; Boolean Algebra; Dense Subspace; Nonempty Open Subset; Complete Boolean Algebra (search for similar items in EconPapers)
Date: 1988
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DOI: 10.1007/978-1-4612-3712-9_6

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