Theoretical analysis demonstrates that compact proximal groups are strongly R-factorizable and omega-narrow, highlighting core topological factorization relationships in proximal group theory.
In recent works, the concept of quotient proximal groups was introduced. This paper introduces the concept of strongly R-factorizable proximal groups and employs the theory of quotient proximal groups to prove an important theorem which states that every compact proximal group is strongly R-factorizable. We also define ω-narrow proximal groups and prove that every strongly R-factorizable proximal group is ω-narrow.
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Kesarwani et al. (2026) studied this question.
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