in this paper, a complete description concerning linear operators of banach spaces with range in lipschitz algebras $lip_al(x)$ is provided. necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. finally, a lower bound for the essential norm of such operators is obtained.

the purpose of this paper is to introduce the concept of pairwise f-closedness in bitopological spaces. this space contains both of pairwise strongcompactness and pairwise s-closedness and contained in pairwise quasi h-closedness. the characteristics and relationships concerning this new class ofspaces with other corresponding types are established. moreover, several ofits basic and important p...

Factorization Machine (FM) is a supervised learning approach with a powerful capability of feature engineering. It yields state-ofthe-art performance in various batch learning tasks where all the training data is made available prior to the training. However, in real-world applications where the data arrives sequentially in a streaming manner, the high cost of re-training with batch learning al...

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

We show that if X is a L∞-space with the Dieudonnè property and Y is a Banach space not containing l1, then any operator T : X⊗ Y → Z, where Z is a weakly sequentially complete Banach space, is weakly compact. Some other results of the same kind are obtained. Let X be a L∞-space (see [1] for this notion and some useful results on L∞-spaces) and Y be a Banach space not containing l1.We consider ...

In this note, we prove that H is a g-closed subgroup of the compact group K if and only if every sequentially continuous character of the dual of H is continuous-in other words, if the dual of H is a so-called sk-group. We conclude that every countable subgroup of a compact group is g-closed, and thus give a positive answer to a problem of Dikranjan, Milan and Tonolo. We also show that the rela...

The distribution and quantitation of enteroviruses among water, suspended solids, and compact sediments in a polluted estuary are described. Samples were collected sequentially from water, suspended solids, fluffy sediments (uppermost layer of bottom sediments), and compact sediment. A total of 103 samples were examined of which 27 (26%) were positive for virus. Polioviruses were recovered most...

Given a Hausdorff uniform space $$X$$ with the countable gage of pseudometrics uniformity , we introduce concept approximate variation function $$f$$ mapping subset $$T$$ reals into : this is infimum family Jordan-type variations all functions $$g:T\to X$$ which differ from in each pseudometric, generated by pseudometric gage, not greater than $$\varepsilon>0$$ . We prove following compactness ...