Scattered Spaces 3
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چکیده
منابع مشابه
Complex Function Algebras and Removable Spaces
The compact Hausdorff space X has the Complex Stone-Weierstrass Property (CSWP) iff it satisfies the complex version of the Stone-Weierstrass Theorem. W. Rudin showed that all scattered spaces have the CSWP. We describe some techniques for proving that certain non-scattered spaces have the CSWP. In particular, if X is the product of a compact ordered space and a compact scattered space, then X ...
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We show that if we interpret modal diamond as the derived set operator of a topological space, then the modal logic of Stone spaces is K4 and the modal logic of weakly scattered Stone spaces is K4G. As a corollary, we obtain that K4 is also the modal logic of compact Hausdorff spaces and K4G is the modal logic of weakly scattered compact Hausdorff spaces. §
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We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as M S. We discuss some closure properties of M S, and show that some simply defined compact spaces, such as compact ordered spaces or compact scattered spaces, are in M S. Most of the basic theory for regular measures is true just in ZF C. On the other hand...
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تاریخ انتشار 2007