we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

in this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

In this paper we describe a family of open questions concerning strong completeness properties associated with the Baire Category Theorem. Some of our questions deal with classical completeness topics such as de Groot’s subcompactness property and the property now called Choquet completeness, while others ask about more recent topics such as domain-representability and its relation to classical...

On $(X,\omega)$ compact K\"ahler manifold, given a model type envelope $\psi\in PSH(X,\omega)$ (i.e. singularity type) we prove that the Monge-Amp\`ere operator is an homeomorphism between set of $\psi$-relative finite energy potentials and measures endowed with their strong topologies as coarsest refinements weak such relative energies become continuous. Moreover, totally ordered family $\math...

employing the notions of the strong $l$-topology introduced by zhangand the $l$-frame introduced by yao  and the concept of $l$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf st$l$-top} of strong$l$-topological spaces, {bf s$l$-loc} of strict $l$-locales and{bf $l$-entopsys} of $l$-enriched topological systems. all of theseconcepts are ...