Proximal and Semi-proximal Spaces
نویسندگان
چکیده
Proximal and semi-proximal spaces are defined with the help of a game played on uniform spaces. Proximal spaces are where the entourage-picker has a winning strategy, and semi-proximal spaces are where the opponent, the point-picker, does not have a winning strategy. The class of proximal spaces is closed under Σ-products and closed subspaces. In this paper it is shown that product of two semi-proximal spaces need not be semi-proximal; that every proximal space is strongly monolithic, (i.e., every countable subspace has metrizable closure); and that every every semi-proximal space is Fréchet and α2. Twenty problems are posed, all but one of them unsolved. Some of these relate to the concept of a uniform box product.
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