We show that the Lipschitz structure of a separable quasi-Banach space does not determine, in general, its linear structure. Using the notion of the Arens-Eells p-space over a metric space for 0 < p ≤ 1 we construct examples of separable quasi-Banach spaces which are Lipschitz isomorphic but not linearly isomorphic.

Abstract Almost s s -mappings and almost compact mappings have been introduced studied. In this article, we continue to research some questions related the -images (resp., images) of metric spaces. The following results are obtained. (1) A space X X is a quotient image if only sequential having c</m:...

in this paper, we  study the arens regularity properties of module actions. we investigate some properties of topological centers of module actions ${z}^ell_{b^{**}}(a^{**})$ and  ${z}^ell_{a^{**}}(b^{**})$ with some conclusions in group algebras.

The plactic monoid is the quotient of the free monoid by the congruence generated by Knuth’s well-celebrated rules. It is well-known that the set of Young tableaux is a cross-section of this congruence which happens to be regular. The main result of this work shows that the set of alphabetically minimal elements in the congruence classes is also regular. We give a full combinatorial characteriz...

for 1 ≤ i ≤ m. Suppose that P ⊂ R is a regular prime (R/P is a regular local ring) and 0 6= f ∈ P . The regular local ring R1 = R[ P f ]m where m is a maximal ideal of R[ P f ] containing mR is called a monoidal transform of R. Suppose that V is a valuation ring of the quotient field of S which dominates S (and thus dominates R). Then given a regular prime P of R (or of S) there exists a unique...

We show that a non-expansive action of a topological semigroup S on a metric space X is linearizable iff its orbits are bounded. The crucial point here is to prove that X can be extended by adding a fixed point of S, thus allowing application of a semigroup version of the Arens-Eells linearization, iff the orbits of S in X are bounded.

The partial derivative automaton (Apd) is usually smaller than other nondeterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton (Apos). By estimating the number of regular expressions that have ε as a partial derivative, we compute a lower bound of the average number of mergings of states in Apos and describe its asymptotic...