A (Hausdorff) topological group is said to have a 𝔊-base if it admits a base of
neighbourhoods of the unit, ${U_ {α}: α∈ ℕ^{ℕ}} $, such that $ U_ {α}⊂ U_ {β} $ whenever …

Malykhin's problem - ScienceDirect Skip to main contentSkip to article Elsevier logo Journals &
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Abstract Motivated from [31], call a precompact group topology τ on an abelian group G ss-
precompact (abbreviated from single sequence precompact) if there is a sequence u=(un) in …

Invariant ideal axiom, beyond the countable sequential groups Page 1 FUNDAMENTA
MATHEMATICAE 265 (2024) Invariant ideal axiom, beyond the countable sequential groups by …

Coarse Geometry Coarse geometry is the study of the large scale geometric features of a
space or, more precisely, of those properties that are invariant up to “uniformly bounded …

We introduce and prove the consistency of a new set theoretic axiom we call the Invariant
Ideal Axiom. The axiom enables us to provide (consistently) a full topological classification of …

This chapter deals with several concepts related with networks with applications both in
Topology and Functional Analysis. Especially we will discuss this concepts for topological …

We survey recent developments concerning the role of convergent sequences in topological
groups. We present the Invariant Ideal Axiom and announce its effect on convergence …

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We investigate precompact topological groups with topologies determined by convergent
sequences (sequential and Fréchet) and show that some natural constructions of such …