Abstract For a non-empty set X X , denote the full transformation semigroup on by T ( ) T\left(X) and suppose that E E is an equivalence relation . Evidently, xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> ∗</m...

Let $f\_i\colon X \rightarrow \mathbf{C}$ , for $i$ integer between $1$ and $p$ be analytic functions defined on a complex variety $X$. us consider $\mathcal{D}\_X$ the ring of linear differential operators $\mathcal{D}\_X \[s\_1, \ldots, s\_p] = \mathbf{C}X \otimes{\mathbf{C}} \mathcal{D}\_X$. $m$ section holonomic -module. We denote $\mathcal{B}(m, x\_0, f\_1, f\_p)$ ideal $\mathbf{C} s\_p]$ ...

A space $X$ is said to have the set star Hurewicz property if for each nonempty subset $A$ of and sequence $(\mathcal{U}_n: n\in \mathbb{N})$ collections sets open in such that $n\in \mathbb N$, $\overline{A} \subset \cup \mathcal{U}_n$, there a $(\mathcal{V}_n: n \in $n \mathbb{N}$, $\mathcal{V}_n$ finite $\mathcal{U}_n$ $x A$, {\rm St}(\cup\mathcal{V}_n, \mathcal{U}_n)$ all but finitely many ...

Abstract The family ${\mathcal{R}} X^*$ of regular subsets the free monoid $X^*$ generated by a finite set X is standard example ${}^*$ -continuous Kleene algebra. Likewise, ${\mathcal{C}} context-free $\mu$ Chomsky algebra, i.e. an idempotent semiring that closed under well-behaved least fixed-point operator . For arbitrary monoids M , M$ closure ${\mathcal{R}}M$ as more briefly, We provide al...

We introduce the strong Gelfand–Phillips property for locally convex spaces and give several characterizations of this property. characterize among admitting a stronger Banach space topology. If $$C_{\mathcal {T}}(X)$$ is continuous functions on Tychonoff X, endowed with topology $${\mathcal {T}}$$ between pointwise compact-open topology, then: (a) has iff X contains compact countable subspace ...

Abstract Let R be a finite commutative ring. The set $${{\mathcal{F}}}(R)$$ F ( R ) of polynomial functions on is ring with pointwise operations. Its group units $${{\mathcal{F}}}(R)^\times $$ × j...

suppose $pi:mathcal{a}rightarrow mathcal{b}$ is a surjective unital $ast$-homomorphism between c*-algebras $mathcal{a}$ and $mathcal{b}$, and $0leq aleq1$ with $ain  mathcal{a}$. we give a sufficient condition that ensures there is a proection $pin mathcal{a}$ such that $pi left( pright) =pi left( aright) $. an easy consequence is a result of [l. g. brown and g. k. pedersen, c*-algebras of real...

Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

‎let $mathcal{a}$ be a unital banach algebra‎, ‎$mathcal{m}$ be a left $mathcal{a}$-module‎, ‎and $w$ in $mathcal{z}(mathcal{a})$ be a left separating point of $mathcal{m}$‎. ‎we show that if $mathcal{m}$ is a unital left $mathcal{a}$-module and $delta$ is a linear mapping from $mathcal{a}$ into $mathcal{m}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a jordan left de...

In the above article [1] , model in ref-type="disp-formula" rid="deqn1" xmlns:xlink="http://www.w3.org/1999/xlink">(1) should be revised as \begin{equation*}\min _{\mathcal{I}...