Algebraic structures on the Cantor set
Keywords:
Baire space, strongly homogeneous space, rectifiable space, retract of group, separable metrizable zero-dimensional space, right topological groupAbstract
Below, by space we mean a separable metrizable zero-dimensional space. It is studied when a space can be embedded in a Cantor set while maintaining the algebraic structure. Main results of the work: every space is an open retract of a Boolean precompact group; every strongly homogeneous space is rectifiable. In this case, the space can be embedded in the Cantor set with the preservation of the algebraic structure. An example of a strongly homogeneous space is constructed which do not admit the structure of a right topological group.
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