In this paper, the concept of {sl local base with  stratifiedstructure} in $I$-topological vector spaces is introduced. Weprove that every $I$-topological vector space has a balanced localbase with stratified structure. Furthermore, a newcharacterization of $I$-topological vector spaces by means of thelocal base with stratified structure is given.

Defining space by dividing it to inside and outside is one of human’s ways to recognize his positionin environment. Architecture is created to response to this need for inside/outside spaces. Design of inside and outsideSpaces and relation between them always has been one of necessities for definition and limitation of human livingspaces, but little attention to relation of this two spatial rea...

in this paper, a new method was proposed for the navigation of a mobile robot in an unknown dynamic environment. the robot could detect only a limited radius of its surrounding with its sensors and it went on the shortest null space (sns) toward the goal. in the case of no obstacle, sns was a direct path from the robot to goal; however, in the presence of obstacles, sns was a space around the r...

A Banach space $X$ has the $Mazur$-$Ulam$ $property$ if any isometry from unit sphere of onto other $Y$ extends to a linear spaces $X,Y$. is called $smooth$ ball unique supporting functional at each point sphere. We prove that non-smooth 2-dimensional Mazur-Ulam property.