Compactness, connectedness and Countability properties of C(X) with the r-topology

Azarpanah, F.; Paimann, M.; Salehi, A.R.

doi:10.1007/s10474-015-0509-6

Acta Math. Hungar.

2015

DOI: 10.1007/s10474-015-0509-6

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Compactness, connectedness and Countability properties of C(X) with the r-topology

F. Azarpanah

M. Paimann

A.R. Salehi

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Cited by 4 publications

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“…Example 3.7. For any strongly zero dimensional topological space X, the ring of all continuous real valued functions C(X) is clean with n ∈ U (C(X)), [6]. So, C(X) and M k (C(X)) are (x 2 − nx)-precious for any k ∈ N by Theorem 3.5 and proposition 2.10.…”

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confidence: 97%

On (weakly) precious rings associated to central polynomials

Khashan¹

2018

B Soc Paran Mat

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Let R be an associative ring with identity and let g(x) be a fixed polynomial over the center of R. We define R to be (weakly) g(x)-precious if for every element a∈R, there are a zero s of g(x), a unit u and a nilpotent b such that (a=±s+u+b) a=s+u+b. In this paper, we investigate many examples and properties of (weakly) g(x)-precious rings. If a and b are in the center of R with b-a is a unit, we give a characterizations for (weakly) (x-a)(x-b)-precious rings in terms of (weakly) precious rings. In particular, we prove that if 2 is a unit, then a ring is precious if and only it is weakly precious. Finally, for n∈ℕ, we study (weakly) (xⁿ-x)-precious rings and clarify some of their properties.

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confidence: 97%

On (weakly) precious rings associated to central polynomials

Khashan¹

2018

B Soc Paran Mat

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The regular topology on C(X, Y)

Jindal

2019

Acta Math. Hungar.

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The regular topology on C(X, Y) revisited

Jindal

2024

Acta Math. Hungar.

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Compactness, connectedness and Countability properties of C(X) with the r-topology

Cited by 4 publications

References 7 publications

On (weakly) precious rings associated to central polynomials

On (weakly) precious rings associated to central polynomials

The regular topology on C(X, Y)

The regular topology on C(X, Y) revisited

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