Abstract Many authors consider that the main pillars of Functional Analysis are Hahn–Banach Theorem, Uniform Boundedness Principle and Open Mapping Principle. The first one is derived from Zorn’s Lemma, while latter two usually obtained Baire’s Category Theorem. In this paper we show these three should be either just or at least eight, since Principle, another five theorems equivalent, as in a ...

In this article we introduce a dual of the uniform boundedness principle which does not require completeness and gives an indirect means for testing set. The principle, although known to analyst despite its applications in establishing results such as Hellinger--Toeplitz theorem, is often missing from elementary treatments functional analysis. Example 1 indicate connection between question spir...

A group G is called bounded if every conjugation-invariant norm on has finite diameter. We introduce various strengthenings of this property and investigate them in several classes groups including semisimple Lie groups, arithmetic linear algebraic groups. provide applications to Hamiltonian dynamics.

(1) ∀u, k∀v ≤ρ tuk∃w A0(u, k, v, w), where A0 is a quantifier–free formula 1 (containing only u, k, v, w as free variables) in the language of a suitable subsystem T ω of arithmetic in all finite types, t is a closed term and ≤ρ is defined pointwise (ρ being an arbitrary finite type). Lets suppose that (1) is provable in T . Then from a given such proof one can extract an effective uniform boun...

The information boundedness principle for rule based inference process requires that the knowledge obtained as a result of a rule should not have more information than that contained in the consequent of this rule. We formulate the information boundedness principle for aggregation and show that it can be expressed using the notion of dominance. We also investigate conditions under which this pr...