Ompactification of Completely Regular Frames based on their Cozero Part

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Abedi Mostafa; ESTAJI ALI AKBAR

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Journal: MATHEMATICAL RESEARCHES Year:2019 | Volume:5 | Issue:1 Page(s): 53-66

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Information Journal Paper

Title

Ompactification of Completely Regular Frames based on their Cozero Part

Author(s)

Abedi Mostafa | ESTAJI ALI AKBAR | Issue Writer Certificate

Keywords

CompactificationQ1

Completely regular frameQ1

Regular idealQ1

Cozero part of a frameQ1

Stone–Čech compactificationQ1

Abstract

Let L be a frame. We denoted the set of all Regular ideals of cozL by rId(cozL). The aim of this paper is to study these ideals. For a frame L, we show that rId(cozL) is a compact Completely regular frame and the map jc: rId(cozL)→ L given by jc (I)=⋁ I is a Compactification of L which is isomorphism to its Stone– Č ech Compactification and is proved that jc have a right adjoint rc: L → rId(cozL), given by rc(a)={x∈ cozL: x≺ ≺ a}. Moreover we identify prime and compact elements of rId(cozL) and we investigate the relation between Regular ideals of cozL and P-frames. In addition it is shown that a frame L is a P-frame if and only if any ideal of cozL is regular.

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APA: Copy

Abedi, Mostafa, & ESTAJI, ALI AKBAR. (2019). Ompactification of Completely Regular Frames based on their Cozero Part. MATHEMATICAL RESEARCHES, 5(1 ), 53-66. SID. https://sid.ir/paper/260771/en

Vancouver: Copy

Abedi Mostafa, ESTAJI ALI AKBAR. Ompactification of Completely Regular Frames based on their Cozero Part. MATHEMATICAL RESEARCHES[Internet]. 2019;5(1 ):53-66. Available from: https://sid.ir/paper/260771/en

IEEE: Copy

Mostafa Abedi, and ALI AKBAR ESTAJI, “Ompactification of Completely Regular Frames based on their Cozero Part,” MATHEMATICAL RESEARCHES, vol. 5, no. 1 , pp. 53–66, 2019, [Online]. Available: https://sid.ir/paper/260771/en

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