T0-Closure Operators and Pre-Orders
- Authors: Venkateswarlu B.1, Swamy U.M.1
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Affiliations:
- Department of Mathematics
- Issue: Vol 39, No 9 (2018)
- Pages: 1446-1452
- Section: Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
- URL: https://journals.rcsi.science/1995-0802/article/view/203636
- DOI: https://doi.org/10.1134/S1995080218090329
- ID: 203636
Cite item
Abstract
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.
About the authors
B. Venkateswarlu
Department of Mathematics
Author for correspondence.
Email: bvlmaths@gmail.com
India, Benguluru Rural, Karnatka, 561 203
U. M. Swamy
Department of Mathematics
Email: bvlmaths@gmail.com
India, Visakhapatnam, Andhra Pradesh, 530 003