Modal Logics of Submaximal and Nodec Spaces
نویسندگان
چکیده
In this note we investigate modal logics of submaximal and nodec spaces when the modal diamond is interpreted as the closure operator of a topological space. We axiomatize the modal logic of nodec spaces. We show that the modal logic of submaximal spaces is a proper extension of the modal logic of nodec spaces, axiomatize it, and prove that it coincides with the modal logics of door spaces and I-spaces. We also show that the modal logic of maximal spaces is a proper extension of the modal logic of submaximal spaces, axiomatize it, and prove that it coincides with the modal logic of perfectly disconnected spaces.
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