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Community Bot
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There seems to be some literature on this already: this paper introduces the notion of a "connective space", i.e., a set equipped with a "connectology", and develops some theory. There was some related Mathematics Stackexchange discussion herehere which connects up with the nontrivial property mentioned by Eric Wofsey in a comment below the question.

There seems to be some literature on this already: this paper introduces the notion of a "connective space", i.e., a set equipped with a "connectology", and develops some theory. There was some related Mathematics Stackexchange discussion here which connects up with the nontrivial property mentioned by Eric Wofsey in a comment below the question.

There seems to be some literature on this already: this paper introduces the notion of a "connective space", i.e., a set equipped with a "connectology", and develops some theory. There was some related Mathematics Stackexchange discussion here which connects up with the nontrivial property mentioned by Eric Wofsey in a comment below the question.

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Todd Trimble
Todd Trimble
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There seems to be some literature on this already: this paper introduces the notion of a "connective space", i.e., a set equipped with a "connectology", and develops some theory. There was some related Mathematics Stackexchange discussion here which connects up with the nontrivial property mentioned by Eric Wofsey in a comment below the question.