Topology, logic and set theory I

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2009-08-20T16:39:43Z

Authors

Miller, Gary G.

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Abstract

Standard topology is formulated in terms of the adherence of one subspace to another. Equivalently, this can be expressed in terms of the (asymmetric) separation of one subspace from another. A single intuitive axiom suffices. This abstractly characterizes "adherence" as a relational morphism which associates "union" with "or" and "arbitrary union" with "existential quantification." A function turns out to be continuous just in case it preserves adherence.

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