EuDML | Browse

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 $ℓ$ -groups of rational valued functions

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

Czechoslovak Mathematical Journal

Usually, an abelian $ℓ$ -group, even an archimedean $ℓ$ -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 $ℓ$ -groups with weak unit which are “ $ℚ$ -convex”. ( $ℚ$ is the group of rationals.) Any $C (X, ℚ)$ is $ℚ$ -convex and its unique $a$ -closure is the Alexandroff algebra of functions on $X$ defined from the clopen sets; this is sometimes $C (X)$ .

Unique covering on radical classes of $ℓ$ -groups

Yue Hui Zhang (1995)

Czechoslovak Mathematical Journal

Uniquely covered radical classes of $ℓ$ -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 $σ$ .

Unital Embedding and Complexification of F-Algebras.

F. Beukers, C. Huijsmans, B.de Pagter (1983)

Mathematische Zeitschrift

Currently displaying 1 – 20 of 22

Page 1 Next