TOPOLOGY FIELDS, TOPOLOGICAL FLOWS AND TOPOLOGICAL ORGANISMS

• 발행기관: 충청수학회
• 저자명: Jae-Ryong Kim
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 26, No. 1, 53~69쪽, 전체 17쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2013.02.28

영문 초록

Topology may described a pattern of existence of ele- ments of a given set X. The family ¿ (X) of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ¿ (X) using a topology on X and regard ¿ (X) a topological space. A topology ¿ on X can be regarded a map from X to ¿ (X) naturally. Such a map will be called topology ¯eld. Similarly we can also de¯ne pe-topology ¯eld. If X is a topological °ow group with acting group T, then naturally we can get a another topological°ow ¿ (X) with same acting group T. If the topological °ow X is minimal, we can prove ¿ (X) is also minimal. The disjoint unions of the topological spaces can describe some topological systems (topological organisms). Here we will give a de¯nition of topological organism. Our purpose of this study is to describe some properties concerning patterns of relationship be-tween topology ¯elds and topological organisms.

목차

1. Introduction

2. Topology ¯elds and pe-topology ¯elds on X.

3. Topological °ow (X; T; ¼) and topologies on X

4. Topology ¯elds and topological organism