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Uniform topology onEQ-algebras

Jiang Yang, Xiao Long Xin, Peng Fei He (2017)

Open Mathematics

In this paper, we use filters of an EQ-algebra E to induce a uniform structure (E, 𝓚), and then the part 𝓚 induce a uniform topology 𝒯 in E. We prove that the pair (E, 𝒯) is a topological EQ-algebra, and some properties of (E, 𝒯) are investigated. In particular, we show that (E, 𝒯) is a first-countable, zero-dimensional, disconnected and completely regular space. Finally, by using convergence of nets, the convergence of topological EQ-algebras is obtained.

Unique a -closure for some -groups of rational valued functions

Anthony W. Hager, Chawne M. Kimber, Warren W. McGovern (2005)

Czechoslovak Mathematical Journal

Usually, an abelian -group, even an archimedean -group, has a relatively large infinity of distinct a -closures. Here, we find a reasonably large class with unique and perfectly describable a -closure, the class of archimedean -groups with weak unit which are “ -convex”. ( is the group of rationals.) Any C ( X , ) is -convex and its unique a -closure is the Alexandroff algebra of functions on X defined from the clopen sets; this is sometimes C ( X ) .

Uniquely covered radical classes of -groups

Y. Zhang, Y. Wang (2001)

Czechoslovak Mathematical Journal

It is proved that a radical class σ of lattice-ordered groups has exactly one cover if and only if it is an intersection of some σ -complement radical class and the big atom over σ .

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