Extensions and Absolutes of Hausdorff Spaces is popular PDF and ePub book, written by Jack R. Porter in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Extensions and Absolutes of Hausdorff Spaces can be Read Online from any device for your convenience.
Extensions and Absolutes of Hausdorff Spaces Book PDF Summary
An extension of a topological space X is a space that contains X as a dense subspace. The construction of extensions of various sorts - compactifications, realcompactifications, H-elosed extension- has long been a major area of study in general topology. A ubiquitous method of constructing an extension of a space is to let the "new points" of the extension be ultrafilters on certain lattices associated with the space. Examples of such lattices are the lattice of open sets, the lattice of zero-sets, and the lattice of elopen sets. A less well-known construction in general topology is the "absolute" of a space. Associated with each Hausdorff space X is an extremally disconnected zero-dimensional Hausdorff space EX, called the Iliama absolute of X, and a perfect, irreducible, a-continuous surjection from EX onto X. A detailed discussion of the importance of the absolute in the study of topology and its applications appears at the beginning of Chapter 6. What concerns us here is that in most constructions of the absolute, the points of EX are certain ultrafilters on lattices associated with X. Thus extensions and absolutes, although very different, are constructed using similar tools.
Detail Book of Extensions and Absolutes of Hausdorff Spaces PDF
- Author : Jack R. Porter
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9781461237129
- Genre : Mathematics
- Total Page : 869 pages
- Language : English
- PDF File Size : 10,9 Mb
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