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Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. A topology ${\tau}$ on X can be regarded a map from X to ${\tau}(X)$ naturally. Such a map will be called topology field. Similarly we can also define pe-topology field. If X is a topological flow group with acting group T, then naturally we can get a another topological flow ${\tau}(X)$ with same acting group T. If the topological flow X is minimal, we can prove ${\tau}(X)$ is also minimal. The disjoint unions of the topological spaces can describe some topological systems (topological organisms). Here we will give a definition of topological organism. Our purpose of this study is to describe some properties concerning patterns of relationship between topology fields and topological organisms.
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참고문헌 (11)
참고문헌 신청
J. Auslander / 1970 / Homomorphisms Of Minimal Transformation Groups / Topology 9:195~203
J. Auslander / 1988 / Minimal Flows and Their Extensions / North-Holland Mathemat-ics Studies 153
R. Ellis / 1969 / Lectures on Topological Dynamics / W. A. Benjamin, Inc
D. H. Gottlieb / Lectures on Vector Fields and the Unity of Mathematics / Preprint
G. GrÄatzer / 1978 / General Lattice Theory / BirkhÄauser
J. Auslander / 1988 / Minimal Flows and Their Extensions / North-Holland Mathemat-ics Studies 153
R. Ellis / 1969 / Lectures on Topological Dynamics / W. A. Benjamin, Inc
D. H. Gottlieb / Lectures on Vector Fields and the Unity of Mathematics / Preprint
G. GrÄatzer / 1978 / General Lattice Theory / BirkhÄauser
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