期刊
ARCHIVE FOR MATHEMATICAL LOGIC
卷 62, 期 7-8, 页码 941-945出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00153-023-00875-5
关键词
o-Minimal theory; Definable Tietze extension property
类别
The two assertions, one about a definable bijection between bounded and unbounded intervals, and the other about the existence of definable continuous extensions for functions defined on closed subsets, are equivalent for an o-minimal expansion of an ordered group M.
The following two assertions are equivalent for an o-minimal expansion of an ordered group M = (M, <, +, 0, ...). There exists a definable bijection between a bounded interval and an unbounded interval. Any definable continuous function f : A ? M defined on a definable closed subset of M-n has a definable continuous extension F:M-n ? M.
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