TITLE:
New Necessary Conditions for a Fixed-Point of Maps in Non-Metric Spaces
AUTHORS:
Ivan Raykov
KEYWORDS:
Topological Space, Compact Metric Space, Fixed Point, Contraction Map, Non-Metric Space
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.12 No.10,
October
18,
2022
ABSTRACT: Our purpose is to introduce new necessary conditions for a fixed point of maps on non-metric spaces. We use a contraction map on a metric topological space and a lately published definition of limit of a function between the metric topological space and the non-metric topological space. Then we show that we can create a function h on the non-metric space Y, h :Y →Y and present necessary conditions for a fixed point of this map on this map on Y. Therefore, this gives an opportunity to take a best conclusion in some sense, when non-metrizable matter is under consideration.