Focal Function in i-Topological Spaces via Proximity Spaces

Abstract

Through the characteristic and properties of ideal we were able to give a new definition to neighborhood of a certain point, but these neighborhoods do not necessarily contain that point. we also introduced a new definition to the local function by using both proximity relation and the idea of the neighborhoods that were indicated, finally we presented most important results and their properties.

Follower and Takeoff Points in Proximity Spaces

“…These points were also studied on different areas such as soft spaces [2][3][4] and fuzzy spaces, the researchers were able to find other parallel definitions [5][6][7]. Some of them studied these points on proximity spaces, specifically in the (𝑖-topological Proximity Space) [8][9][10][11]. The proximity space established by Riesz (1908), which is synonymous with the measurement between two sets, has inspired researchers to study those points within this space due to its important applications in image processing and lost image retrieval, as well as its importance in engineering applications [12].…”