The pointfree version of 𝓒c(X) via the ranges of functions
-
Maryam Taha
and
Maryam Robat Sarpoushi
Abstract
Let Rα := {r ∈ ℝ : coz(α − r) ≠ → p} for every α ∈ 𝓡(L). The ring 𝓒c (L) is introduced as a pointfree version of the subring 𝓒c(X) of C(X) by Rα. In this paper, we show that 𝓒c(X) is a z-good ring and every radical ideal in it is an absolutely convex ideal. Also, we study this result which for any frame L, there exists a zero-dimensional frame M, which is a continuous image of L and 𝓒c(L) ≅ 𝓒c(M).
Acknowledgement
We would like to express our deep gratitude to the referee for improving the article with useful comments.
(Communicated by Tomasz Natkaniec)
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Articles in the same Issue
- Prof. RNDr. Gejza Wimmer, DrSc. – 3/4 C?
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- The pointfree version of 𝓒c(X) via the ranges of functions
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- Subordination properties and coefficient problems for a novel class of convex functions
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- Fourth-order nonlinear strongly non-canonical delay differential equations: new oscillation criteria via canonical transform
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- On lower density operators
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- On the von Bahr–Esseen inequality for pairwise independent random vectors in Hilbert spaces with applications to mean convergence
- Large deviations for some dependent heavy tailed random sequences
- Metric, stratifiable and uniform spaces of G-permutation degree
- In memory of Paolo
Articles in the same Issue
- Prof. RNDr. Gejza Wimmer, DrSc. – 3/4 C?
- On hyper (r, q)-Fibonacci polynomials
- The pointfree version of 𝓒c(X) via the ranges of functions
- On the x-coordinates of Pell equations that are products of two Pell numbers
- Subordination properties and coefficient problems for a novel class of convex functions
- Certain radii problems for 𝓢∗(ψ) and special functions
- On direct and inverse Poletsky inequalities with a tangential dilatation
- Fourth-order nonlinear strongly non-canonical delay differential equations: new oscillation criteria via canonical transform
- Hermite interpolation of type total degree associated with certain spaces of polynomials
- Decomposition in direct sum of seminormed vector spaces and Mazur–Ulam theorem
- A fixed point technique to the stability of Hadamard 𝔇-hom-der in Banach algebras
- Compact subsets of Cλ,u(X)
- Variations of star selection principles on hyperspaces
- On lower density operators
- Gröbner bases in the mod 2 cohomology of oriented Grassmann manifolds G͠2t,3
- On the von Bahr–Esseen inequality for pairwise independent random vectors in Hilbert spaces with applications to mean convergence
- Large deviations for some dependent heavy tailed random sequences
- Metric, stratifiable and uniform spaces of G-permutation degree
- In memory of Paolo
