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Given a free ultrafilter on and a space , we say that is the -limit point of a sequence in (in symbols, -) if for every neighborhood of , . By using -limit points from a suitable metric space, we characterize the selective ultrafilters on and the -points of . In this paper, we only consider dynamical systems , where is a compact metric space. For a free ultrafilter on , the function is defined by - for each . These functions are not continuous in general. For a...
For a cardinal , we say that a subset of a space is -compact in if for every continuous function , is a compact subset of . If is a -compact subset of a space , then denotes the degree of -compactness of in . A space is called -pseudocompact if is -compact into itself. For each cardinal , we give an example of an -pseudocompact space such that is not pseudocompact: this answers a question posed by T. Retta in “Some cardinal generalizations of pseudocompactness”...
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