We prove that the restriction of a given orthogonal-complete metric space to the closure of the orbit induced by the origin point with respect to an orthogonal-preserving and orthogonal-continuous map is a complete metric space. Then we show that many existence results on fixed points in orthogonal-complete metric spaces can be proved by using the corresponding existence results in complete metric spaces.

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关于正交完全度量空间的注释

我们证明了给定正交完备度量空间对由原点引起的关于正交保持和正交连续映射的轨道闭合的限制是完备度量空间。然后我们证明了正交完备度量空间中不动点上的许多存在性结果可以利用完备度量空间中相应的存在性结果来证明。