Noori Al-Mayahi - Mathematics Department, College of Science, Al-Qadisiyah University, Iraq
Haitham Mosa - Mathematics Department, College of Science, Al-Qadisiyah University, Iraq

In this paper, we presented both the concept of  Daniell space and the extension of Daniell space with some basic results related to these spaces when the Daniell functional on a Banach lattice space.  The extension of Daniell's space has been proven a complete space.

Daniell space, Riesz space, Banach lattice, normed space, Banach space, complete