The concept of -closedness, a kind of covering property for topological spaces, has already been studied with meticulous care from different angles and via different approaches. In this paper, we continue the said investigation in terms of a different concept viz. grills. The deliberations in the article include certain characterizations and a few necessary conditions for the -closedness of a space, the latter conditions are also shown to be equivalent to -closedness in a - almost regular space. All these and the associated discussions and results are done with grills as the prime supporting tool.

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise near compact and fibrewise locally near compact spaces, which are generalizations of well-known concepts near compact and locally near compact topological spaces. Moreover, we study relationships between fibrewise near compact (resp., fibrewise locally near compact) spaces and some fibrewise near separation axioms.

<p>In this paper, we prove there exists a coupled fixed point for a set- valued contraction mapping defined on X× X , where X is incomplete ordered G-metric. Also, we prove the existence of a unique fixed point for single valued mapping with respect to implicit condition defined on a complete G- metric.</p>

   The aim of this paper is to introduce and study new class of fuzzy function called fuzzy semi pre homeomorphism in a fuzzy topological space by utilizing fuzzy semi pre-open sets. Therefore, some of their characterization has been proved; In addition to that we define, study and develop corresponding to new class of fuzzy semi pre homeomorphism in fuzzy topological spaces using this new class of functions.

In thisipaper, we introduce the concepts of the modified tupledicoincidence points and the  mixed finiteimonotone property. Also the existenceiand uniquenessiof modified tupled coincidenceipoint is discusses without continuous condition for mappings having imixed finite monotoneiproperty in generalizedimetric spaces.

The primary aim of this paper, is to introduce the rough probability from topological view. We used the Gm-topological spaces which result from the digraph on the stochastic approximation spaces to upper and lower distribution functions, the upper and lower mathematical expectations, the upper and lower variances, the upper and lower standard deviation and the upper and lower r th moment. Different levels for those concepts are introduced, also we introduced some results based upon those concepts.

The research deals with one of the urban problems facing cities, namely the existence of neglected urban spaces that need to be activated , These spaces give a negative image of the city, is not conducive to life and social interactions or the city has a one distinctive urban experience, leading to a reduction peoples' confidence in revisiting of those areas, hinder the rest of the activities in that region . Because these spaces are of the basic components of the city and give it its identity through the elements and entities that constitute it  , The idea of research emerged in the reclaiming of these spaces within contemporary urban trends and the activation of  flexible  , short-term and inovation for that purpose with

In this research, we introduce and study the concept of fibrewise bitopological spaces. We generalize some fundamental results from fibrewise topology into fibrewise bitopological space. We also introduce the concepts of fibrewise closed bitopological spaces,(resp., open, locally sliceable and locally sectionable). We state and prove several propositions concerning with these concepts. On the other hand, we extend separation axioms of ordinary bitopology into fibrewise setting. The separation axioms we extend are called fibrewise pairwise T_0 spaces, fibrewise pairwise T_1 spaces, fibrewise pairwise R_0 spaces, fibrewise pairwise Hausdorff spaces, fibrewise pairwise functionally Hausdorff spaces, fibrewise pairwise regular spaces, fibrewise