Movability and strong Whitney-reversible properties
In [Stud. Topol. Proc. Conf. Charlotte, N. C. 1974, 393-410 (1975; Zbl 0317.54005), Theorem 4 and Example 3], \textit{S. B. Nadler} jun. proved that the property of being locally connected is a sequential strong Whitney- reversible property, and the property of being pathwise connected is not a strong Whitney-reversible property. We show that the property of being (pointed) 1-movable is a sequential strong Whitney-reversible property. As a corollary, the property of being (pointed) movable is a sequential strong Whitney-reversible property for curves. This is an affirmative answer to the author's question in Trans. Am. Math. Soc. 297, 529-546 (1986; Zbl 0607.54014) (5.2). Also, we show that the property of being (nearly) 1-movable is a Whitney property.
sequential strong Whitney- reversible property
scientific article; zbMATH DE number 4084534
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