Extensions and Absolutes of Hausdorff Spaces.pdf

Extensions and Absolutes of Hausdorff Spaces PDF

Jack R. Porter

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.

(PDF) Spaces with Coarser Minimal Hausdorff … A technique is developed, using if-closed extensions, for determining when certain HausdorfF spaces are Katetov, i.e., have a coarser minimal Hausdorff topology.

3.28 MB DATEIGRÖSSE
1461283167 ISBN
Englisch SPRACHE
Extensions and Absolutes of Hausdorff Spaces.pdf

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locally-P extensions of a given locally compact paracompact space X. ... if a Hausdorff space has P, provided that it is the union of a finite collection of its ( closed) ... [16] J. R. Porter and G. Woods, Extensions and Absolutes of Hausdorff Spaces,. Then any extension of f to X is a retraction. Problem 2. A compact Hausdorff space X is called an absolute retract if whenever X is embedded into a normal space ...