in this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. also, we give anew generalization of the mazur-ulam theorem when $x$ is a $2$-fuzzy $2$%-normed linear space or $im (x)$ is a fuzzy $2$-normed linear space, thatis, the mazur-ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...

The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...

In this paper we study bidirectional state space search with consistent heuristics, with a focus on obtaining sufficient conditions for node expansion, i.e., conditions characterizing nodes that must be expanded by any admissible bidirectional search algorithm. We provide such conditions for front-to-front and front-to-end bidirectional search. The sufficient conditions are used to prove that t...

This paper explores the role of Blending Theory, as a framework, to aid in design decisions while deploying mobile experiences for heritage storytelling. Blending Theory provides a structured way of thinking about how digital and physical spaces can be brought together to create new experiences in blended spaces. In this paper we describe the development of an app that aims to enhance the visit...

the concept of ${mathscr{f}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{f}}$. its equivalence to the concept of ${mathscr{f}}$-convergence in uniform spaces is proved. this convergence generalizes many kinds of convergence, including the well-known statistical convergence.

we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

introduction in this paper, a new approach is applied to explain inner interactions in architectural spaces. this approach is recently used in urban design. it has also been used in architecture in this essay to consider the application of mosques_ madrasah in qazvin. this city as instances of salehich and madreseh is proving the interactions between the spaces of masjed-madresse in ghajari maj...