Abstarct: Breaches of gap topology on the space of closed operators recent years widely in different parts of mathematics, including geometry and topology, nonlinear control systems, and analysis of signals and systems plays. It is simple and intuitive gap metric for which the application has many flaws. The first gap metric we penetrate the spaces between the close of a Hilbert space referred, and then we describe basic properties. The particular metric between operators endless leaks and considers new formula for calculating the penetration metric between two densely defined operators to offer packages.