힐버트 규브에 대한 연구

국문 초록 (Abstract)

위상수학은 100여년동안 많은 변화를 가져왔으며 우리가 기존에 알고 있는 유클리드 기하학에 많은 발전을 가져왔다.

위상 공간, 거리공간, 수열의 극한, 유계, 노름공간, 콤팩트 공간의 개념을 알아보도록 하고 분리공간인 space , space , space (Hausdorff) , space (정칙공간) , space (정규공간)에 대하여 알아본다.

유클리드공간과 힐버트 공간에 대하여 알아보고, 힐버트-슈미츠의 작용소에 대하여 정의를 하자.

이고 이라고 주어진다면 이는 힐버트 공간 의 부분집합이 됨을 보이고, 이 때 힐버트 큐브는 폐집합이고 유계인 집합임이 됨을 증명하여 보자.

목차 (Table of Contents)

• 국문요약··································································· 0
• 제 1 장 위상공간························································ 1
• 제 2 장 거리공간························································ 4
• 제 3 장 노름공간························································ 11
• 제 4 장 유클리드 공간과 힐버트 공간······························· 15
• 참 고 문 헌······························································ 26
• Abstract·································································· 27