Nearness structures and proximity extensions

Gagrat, M. S.; Thron, W. J.

doi:10.1090/S0002-9947-1975-0385808-3

Nearness structures and proximity extensions
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by M. S. Gagrat and W. J. Thron PDF

Trans. Amer. Math. Soc. 208 (1975), 103-125 Request permission

Abstract:

Proximity, contiguity and nearness structures are here studied from a unified point of view. In the discussion the role that grills can play in the theory is emphasized. Nearness structures were recently introduced by Herrlich and Naimpally. Thron pointed out the importance of grills in proximity theory. Nearness structures $v$ are then used to generate proximity extensions $(\phi ,({X^v},{\Pi ^v}))$ of a given LO-proximity space $(X,\Pi )$, where ${\Pi _v} = \Pi$. Finally, the relation of the extensions $(\phi ,({X^v},{\Pi ^v}))$ to arbitrary extensions $(i,(Y,{\Pi ^ \ast }))$ is investigated.

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