Basic Topological Concepts and a Construction of Real Numbers in Alternative Set Theory

Alternative set theory (AST) may be suitable for the ones who try to capture objects or phenomenons with some kind of indefiniteness of a border. While AST provides various notions for advanced mathematical studies, correspondence of them to that of conventional ones are not fully developed. This paper presents basic topological concepts in AST, and shows their correspondence with those of conventional ones, and isomorphicity of a system of real numbers in AST to that of conventional ones.