The notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  Probabilistic Metric space was  introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of  probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are  topological vector spaces and the open mapping an...

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

‎A topological space is called submaximal if each of its dense subsets is open and is called nodec if each of its nowhere dense ea subsets is closed‎. ‎Here‎, ‎we study a variety of spaces some of which have already been studied in $C(X)$‎. ‎Among them are‎, ‎most importantly‎, ‎quasi $P$-spaces and pointwise quasi $P$-spaces‎. ‎We obtain some new useful topological characterizations of quasi $...

the urban open space is the context in which the human activities and behavior takes place and the socio-cultural relations of people happen in it. public spaces are places responding to the daily needs and public life in cities. these spaces throughout time and based on the socio-cultural and economic conditions would transform. urban spaces also are places for various activities. in a simple ...

measuring the perceived quality of residential environments is one of the fields of inquiry for housing environment researches. most of the data on the perceived quality of residential environments are restricted to existing and large cities experiences. however, little attention has been paid to new town residential complexes particularly in third world countries. residential and neighborhood ...

Convergence of operators acting on a given Hilbert space is an old and well studied topic in operator theory. The idea of introducing a related notion for operators acting on varying spaces is natural. However, it seems that the first results in this direction have been obtained only recently, to the best of our knowledge. Here we consider sectorial operators on scales of Hilbert spaces. We def...

isovist and visibility graph analysis tools are used to quantify and measure the quality of space, and despite their lack of maturity and evolution, they are considered to be the future of space analysis tools by researchers. this study was undertaken with the purpose of introducing the aforementioned tools for analyzing sanandaj’s urban areas. in this study, four different urban areas in sanan...

A. Csaszar introduced and extensively studied the notion of generalized open sets. Following Csazar, we introduce a new notion hyperconnected. We study some specic properties about connected and hyperconnected in generalized topological spaces. Finally, we characterize the connected component in generalized topological spaces.