SPACES WITH UNIQUE HAUSDORFF EXTENSIONS

被引:1
|
作者
MOONEY, DD [1 ]
机构
[1] WESTERN KENTUCKY UNIV,DEPT MATH,BOWLING GREEN,KY 42101
关键词
EXTENSION; HAUSDORFF; H-CLOSED EXTENSION; H-BOUNDED SET; OPEN FILTER; PRIME OPEN FILTER; LATTICE; SEMILATTICE;
D O I
10.1016/0166-8641(94)00031-W
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
H-closed extensions of Hausdorff spaces have been studied extensively as a generalization of compactifications of Tychonoff spaces. The collection of H-closed extensions of a space is known to have an upper semilattice structure. Little work has been done to characterize spaces whose collections of H-closed extensions have specified upper semilattice structures. In 1970 J.R. Porter found necessary and sufficient conditions on a space so that it would have exactly one one-point H-closed extension. He asked for a characterization of those spaces which have exactly one H-closed extension. This is the same as having exactly one Hausdorff extension. In this paper we answer Porter's question and give an example of such a space. Topological sums of this space give spaces which have two, five, or in general, p(n) many H-closed extensions where p(n) is the number of ways a set of size n can be partitioned. This space is also an example of a space with exactly one free prime open filter which gives an answer to a question asked by J. Pelant, P. Simon, and J. Vaughan. As a preliminary for obtaining the above results, we find necessary and sufficient conditions on a space so that the S- and theta-equivalence relations defined by J.R. Porter and C. Votaw are equivalent.
引用
收藏
页码:241 / 256
页数:16
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