In this paper we investigate the structure of the complete lattice of principal generalized topologies, employing the notion of ultratopology. On any partially ordered set we introduce a generalized topology. The existence of an anti-isomorphism between principal generalized topologies and preorder relations on a set is proposed. After determining the very basic topological properties therein, we will show that each generalized topology has a lattice complement in principal generalized topologies.
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The author would like to thank to the referee for carefully reading the paper and for giving useful comments which will help to improve it.
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Arianpoor, H. On the lattice of principal generalized topologies. Period Math Hung 78, 79–87 (2019). https://doi.org/10.1007/s10998-018-0266-8