The Hyperreals enlargement sets and its application on compact topology - A. Elageili , Dr.Ragab; I. Ali, Mr. Haleemah (مجلة المنارة العلمية, 2024)
This paper presents a study of hyperreal numbers and their relations to real numbers. The hyperreals are a number system extension of the real number system. With this system, simpler and more intuitively natural definition (topological notions of special points and compactness), proofs (Heine-Borel theorem), and new concepts (limited, unlimited numbers, enlargement sets, and halos) of mathematical interest are offered.