2008•Journal of Nanyang Normal UniversityRequires access
Generalize the Lipschitz condition to the metric space
Dang Li-na
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Abstract
In this paper,the Lipschitz condition in calculus is generalized into metric space.Some new results are gained when the mapping in the metric spaces satisfies the Lipschitz condition.A new category Lip is defined by taking all metric spaces as its objects and the mappings satisfying the Lipschitz condition as its morphisms.The product of finite amount of objects in the category Lip is discussed.