Muayad G. Mohsin, New Types of Fixed Points in Operator Topological Space, Journal of Engineering and Applied Sciences, Volume 14,Issue 13, 2019, Pages 4466-4470, ISSN 1816-949x, jeasci.2019.4466.4470, (https://makhillpublications.co/view-article.php?doi=jeasci.2019.4466.4470) Abstract: In this study, we state and prove certain types of fixed point in operator topological spaces. We generalize, the concepts of orbit, periodic and fixed point property in operator topological space, also, we found new concepts in operator theory such as productive spaces and homeomorphism between these space. Keywords: ρ-fixed point;ρ-orbit;ρ-periodic;ρ1 -homeomorphism;composite operator function;topological space