Chu Space
Chu spaces generalize the notion of topological space by dropping the requirements that the set of open sets be closed under union and finite intersection, that the open sets be extensional, and that the membership predicate (of points in open sets) be two-valued. The definition of continuous function remains unchanged other than having to be worded carefully to continue to make sense after these generalizations.
Read more about Chu Space: Definition, Categorical Structure, Variants, Universality
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“Art and power will go on as they have done,—will make day out of night, time out of space, and space out of time.”
—Ralph Waldo Emerson (1803–1882)