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Closure operators and connectedness. (English) Zbl 0791.54001

For constructs \(\mathbb{C}\), the authors introduce the concept of connectedness with respect to a closure operator. They extend several classical topological results to this setting and show that the connectedness-disconnectedness Galois connection factors through the collection of all closure operators in \(\mathbb{C}\).

MSC:

54A05 Topological spaces and generalizations (closure spaces, etc.)
06A15 Galois correspondences, closure operators (in relation to ordered sets)
54D05 Connected and locally connected spaces (general aspects)
18D35 Structured objects in a category (MSC2010)
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