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About: Formal ball     Goto   Sponge   NotDistinct   Permalink

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In topology, a formal ball is an extension of the notion of ball to allow unbounded and negative radius. The concept of formal ball was introduced by Weihrauch and Schreiber in 1981 and the negative radius case (the generalized formal ball) by Tsuiki and Hattori in 2008. Specifically, if is a metric space and the nonnegative real numbers, then an element of is a formal ball. Elements of are known as generalized formal balls. Formal balls possess a partial order defined by if , identical to that defined by set inclusion. Formal balls possess the Lawson topology and the .