Topological representation of some lattices
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Ali Taherifar
and
Mohamad Reza Ahmadi Zand
Abstract
In this paper, we first give a topological representation of some algebraic lattices of ideals of C(X). Next, we apply these results and prove that a space X is normal if and only if the lattice of closed fixed ideals of C(X) is a sublattice of the lattice of ideals of C(X). It is proved that if two rings C(X) and C(Y) are isomorphic, then two lattices Z∘[X] and Z∘[Y] are isomorphic. We conclude that two rings C*(X) and C*(Y) are isomorphic if and only if two lattices Z[βX] and Z[βY] are isomorphic.
Acknowledgement
The authors are grateful to the referee for suggestions that helped improve the presentation of the paper.
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Communicated by L’ubica Holá
References
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© 2024 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Right algebras in Sup and the topological representation of semi-unital and semi-integral quantales, revisited
- Topological representation of some lattices
- Exact-m-majority terms
- Polynomials whose coefficients are generalized Leonardo numbers
- A study on error bounds for Newton-type inequalities in conformable fractional integrals
- Improved conditions for the distributivity of the product for σ-algebras with respect to the intersection
- Close-to-convex functions associated with a rational function
- Complete monotonicity for a ratio of finitely many gamma functions
- Class of bounds of the generalized Volterra functions
- Some new uniqueness and Ulam–Hyers type stability results for nonlinear fractional neutral hybrid differential equations with time-varying lags
- Existence of positive solutions to a class of boundary value problems with derivative dependence on the half-line
- Solving Fredholm integro-differential equations involving integral condition: A new numerical method
- Bounds of some divergence measures on time scales via Abel–Gontscharoff interpolation
- Weighted 1MP and MP1 inverses for operators
- Non-commutative effect algebras, L-algebras, and local duality
- Operator Bohr-type inequalities
- Some results for weighted Bergman space operators via Berezin symbols
- Lower separation axioms in bitopogenous spaces
- Fisher information in order statistics and their concomitants for Cambanis bivariate distribution
- Irreducibility of strong size levels
