Further thoughts on the ring $${\mathcal {R}}_c (L)$$ in frames

Estaji, Ali Akbar; Sarpoushi, Maryam Robat; Elyasi, Mahtab

doi:10.1007/s00012-019-0619-z

Cited by 3 publications

(1 citation statement)

References 17 publications

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“…This subalgebra has more attendance recently; see, for example, [1,4,11,14,17,18]. In [16], the authors introduced and studied the ring R c (L) as the pointfree topology version of C c (X) (see also [6,8,9]). By L c (X), we mean the ring of all continuous functions that C f is dense in X for f ∈ C(X), where C f = {U : U ∈ O(X) and |f (U )| ℵ 0 }; see [15].…”

Section: Introductionmentioning

confidence: 99%

Locally functionally countable subalgebra of $\mathcal{R}(L)$

Elyasi¹,

Estaji²,

Sarpoushi³

2020

Arch. Math. (Brno)

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Let Lc(X) = {f ∈ C(X) : C f = X}, where C f is the union of all open subsets U ⊆ X such that |f (U)| ℵ 0. In this paper, we present a pointfree topology version of Lc(X), named R c (L). We observe that R c (L) enjoys most of the important properties shared by R(L) and Rc(L), where Rc(L) is the pointfree version of all continuous functions of C(X) with countable image. The interrelation between R(L), R c (L), and Rc(L) is examined. We show that Lc(X) ∼ = R c O(X) for any space X. Frames L for which R c (L) = R(L) are characterized.

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Section: Introductionmentioning

confidence: 99%

Locally functionally countable subalgebra of $\mathcal{R}(L)$

Elyasi¹,

Estaji²,

Sarpoushi³

2020

Arch. Math. (Brno)

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Ordered Field Valued Continuous Functions with Countable Range

Acharyya

Ray

Pratip

2021

Bull. Iran. Math. Soc.

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The pointfree version of 𝓒_c(X) via the ranges of functions

Taha,

Estaji,

Sarpoushi

2024

Mathematica Slovaca

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Let R α := {r ∈ ℝ : coz(α − r) ≠ → p} for every α ∈ 𝓡(L). The ring 𝓒 c (L) is introduced as a pointfree version of the subring 𝓒 c (X) of C(X) by R α . In this paper, we show that 𝓒 c (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 𝓒 c (L) ≅ 𝓒 c (M).

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Further thoughts on the ring $${\mathcal {R}}_c (L)$$ in frames

Cited by 3 publications

References 17 publications

Locally functionally countable subalgebra of $\mathcal{R}(L)$

Locally functionally countable subalgebra of $\mathcal{R}(L)$

Ordered Field Valued Continuous Functions with Countable Range

The pointfree version of 𝓒_c(X) via the ranges of functions

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Further thoughts on the ring $${\mathcal {R}}_c (L)$$ in frames

Cited by 3 publications

References 17 publications

Locally functionally countable subalgebra of $\mathcal{R}(L)$

Locally functionally countable subalgebra of $\mathcal{R}(L)$

Ordered Field Valued Continuous Functions with Countable Range

The pointfree version of 𝓒 c (X) via the ranges of functions

Contact Info

Product

Resources

About

The pointfree version of 𝓒_c(X) via the ranges of functions