本文证明了：群、欧几里得空间、距离空间和拓扑空间的公理系统的独立性。
It has been proved that the nature of independence exists in the axiomatic system of Group, Euclidean space, distance space and topological space.
本文的工作表明，欧几里得空间下的佯谬解就是辛空间下的约当型解，而且通过标准的数学方法可以直接获得所有佯谬问题的解析解。
It is revealed that the paradox solution in Euclidean space is just a solution in symplectic space in the Jordan form which can easily be obtained by conventional mathematical means.
本文的工作表明，欧几里得空间下的佯谬解就是辛空间下的约当型解，而且通过标准的数学方法可以直接获得所有佯谬问题的解析解。
It is revealed that the paradox solution in Euclidean space is just a solution in symplectic space in the Jordan form which can easily be obtained by conventional mathematical means.
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