منابع مشابه
POINTWISE PSEUDO-METRIC ON THE L-REAL LINE
In this paper, a pointwise pseudo-metric function on the L-realline is constructed. It is proved that the topology induced by this pointwisepseudo-metric is the usual topology.
متن کاملReflexive Group Topologies on Abelian Groups
It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology. Introduction For a topological group G, the group G of continuous homomorphisms (characters) into the torus T = {z ∈ C : |z| = 1} endowed with the compact-open topology is called the character group of G and G is named Pontryagin reflexive or reflexive if the canonical homomorphism ...
متن کاملImposing pseudocompact group topologies on Abelian groups
The least cardinal λ such that some (equivalently: every) compact group with weight α admits a dense, pseudocompact subgroup of cardinality λ is denoted by m(α). Clearly, m(α) ≤ 2. We show: Theorem 3.3. Among groups of cardinality γ, the group ⊕γQ serves as a “test space” for the availability of a pseudocompact group topology in this sense: If m(α) ≤ γ ≤ 2 then ⊕γQ admits a (necessarily connect...
متن کاملOn the supremum of the pseudocompact group topologies
P is the class of pseudocompact Hausdorff topological groups, and P′ is the class of groups which admit a topology T such that (G,T ) ∈ P. It is known that every G= (G,T ) ∈ P is totally bounded, so for G ∈ P′ the supremum T ∨(G) of all pseudocompact group topologies on G and the supremum T #(G) of all totally bounded group topologies on G satisfy T ∨ ⊆ T #. The authors conjecture for abelian G...
متن کاملMonoid Kernels and Profinite Topologies on the Free Abelian Group
To each pseudovariety of abelian groups residually containing the integers, there is naturally associated a proonite topology on any nite rank free abelian group. We show in this paper that if the pseudovariety in question has a decidable membership problem, then one can eeectively compute membership in the closure of a subgroup and more generally, in the closure of a rational subset of such a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1981
ISSN: 0022-247X
DOI: 10.1016/0022-247x(81)90072-x