Abstract
Abstract Topologies of special type in a product of two topological spaces are introduced and considered here, in a general case, then in ℝ n to finish on the plane. In the last case, the graph of any function is closed in the considered topology, so it leads to interesting examples of open sets. Our purpose is to study properties of these topologies and connections between them. We prove also that every continuous real function from the plane equipped with the considered topology is in the first class of Baire.
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