Weil Nearness Spaces

Jorge Picado

Abstract: In this paper the concept of nearness for spaces is introduced in terms of Weil's notion of entourage, motivated by the study of the corresponding frame-theoretical objects. It is shown that these spaces, although distinct from the classical nearness spaces of Herrlich, also form a nice topological category. Indeed, it is proved that this category contains, as nicely embedded full subcategories, various categories of topological nature such as, for example, the categories of symmetric topological spaces and continuous maps, proximal spaces and proximal maps and uniform spaces and uniformly continuous maps.

Keywords: Nearness space; interior entourage; open entourage; Weil nearness space; symmetric topological space; proximal space; uniform space.

Classification (MSC2000): 06D20, 18B30, 54E05, 54E15, 54E17

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