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Steklov Mathematical Institute Seminar
December 21, 2023 16:00, Moscow, Steklov Mathematical Institute of RAS, Conference Hall (8 Gubkina)
 


On homeomorphisms of Cantor cubes

E. V. Shchepin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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E. V. Shchepin
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Abstract: The Cantor cube is an uncountable degree of the Cantor set. Thus, the Cantor cube of continual weight can be represented as a set of Boolean functions on a segment with a topology of pointwise convergence. The main result of the speaker is to prove the strong homogeneity of Cantor cubes. In particular, it follows that the homeomorphism between any compact subsets of a Cantor cube having a weight less than the cube itself extends to an ambient homeomorphism of the entire cube.
 
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