论文标题
指标空间中的刚性指标
Strongly rigid metrics in spaces of metrics
论文作者
论文摘要
如果指标未两次正距离，则据说公制空间非常刚性。 1972年，贾诺斯（Janos）证明，当且仅当它是零维时，可分离的Metrizable空间具有强烈的刚性度量。在本文中，我们将为指标空间理论发展这一结果。对于一个零维的可衡量空间，我们证明所有强刚性指标的集合在Metics的空间中都很稠密。此外，如果该空间是可计数的紧凑子空间的结合，则该集合是合并的。结果，我们表明，对于强大的零维定空间，所有具有非平凡（生物）自我测量的指标的集合在指标的空间中都是相当的。
A metric space is said to be strongly rigid if no positive distance is taken twice by the metric. In 1972, Janos proved that a separable metrizable space has a strongly rigid metric if and only if it is zero-dimensional. In this paper, we shall develop this result for the theory of space of metrics. For a strongly zero-dimensional metrizable space, we prove that the set of all strongly rigid metrics is dense in the space of metics. Moreover, if the space is the union of countable compact subspaces, then that set is comeager. As its consequence, we show that for a strongly zero-dimensional metrizable space, the set of all metrics possessing no nontrivial (bijective) self-isometry is comeager in the space of metrics.
