Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
It is well known that the lattice of closed subsets of any topological space is isomorphic to that of a T0-topological space. This result is extended to lattices of closed subsets with respect to arbitrary closure operator on a set. Also, we establish a one-to-one correspondence between closure operators which are both algebraic and topological on a given set X and pre-orders on X and prove that this correspondence induces a one-to-one correspondence between topological algebraic T0-closure operators on X and partial orders on X.
Keywords and phrases
Closure operator Moore class algebraic lattice T0-closure operator pre-order
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