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Equivalent metrics and the spans of graphs

L. C. Hoehn, A. Karassev (2009)

Colloquium Mathematicae

We present a result which affords the existence of equivalent metrics on a space having distances between certain pairs of points predetermined, with some restrictions. This result is then applied to obtain metric spaces which have interesting properties pertaining to the span, semispan, and symmetric span of metric continua. In particular, we show that no two of these variants of span agree for all simple closed curves or for all simple triods.

Every Lusin set is undetermined in the point-open game

Ireneusz Recław (1994)

Fundamenta Mathematicae

We show that some classes of small sets are topological versions of some combinatorial properties. We also give a characterization of spaces for which White has a winning strategy in the point-open game. We show that every Lusin set is undetermined, which solves a problem of Galvin.

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