數學的 構造에 관한 硏究

Abstract

現代數學의 發達과 함꼐 그에 따른 數學敎脊育 現代化 運動이 전 세계적으로 전개되고 있고, 이러한 現代數學은 構造主義를 표방하고 있다. 1950年代까지의 現代數學은 個個의 數學的體系의 構造를 究明하는 것을 목표로 하였다. 따라서 本 論文에서는 數學的構造 가운데서 代數的構造(Alge-braic structure), 位相的構造(Topological structure)과 다음과 같이 정리하였다. (1) 代數的構造에서는 演算, 群, 環, 整域, 體의 槪念을 알아 보았다. (2) 位相的構造에서는 位相空間, 分離公理에서의 空間, 距離空間, 一樣空間을 알아 보았다. (3) 一樣空間을 이루는 조건①∼⑤가 論理的으로 독립임을 알아 보았다.;The modernization movement of mathematics is spreading all over the world with its modern development. This modern mathematics has adopted a slogan of structuralism. Till the middle of the twentieth century, the aim of mathematics has been the investigation of its systematic structure. Mathematic structures are devided into algebratic, topological and order structure. In this study, two of them, algebraic and topological structure were studied as follows: 1. In algebraic structure, the conception of operation, group, ring, integral domain and field were studied. 2. In topolpgical structure, topological space, space of axiom of seperation, metric space and uniform space were studied. 3. The fact that five conditions of uniform space are from each other was found.