Borel measurable Hahn-Mazurkiewicz theorem
نویسندگان
چکیده
It is well known due to Hahn and Mazurkiewicz that every Peano continuum a continuous image of the unit interval. We prove an assignment, which takes as input produces output mapping whose range continuum, can be realized in Borel measurable way. Similarly, we find assignment any nonempty compact metric space assigns from Cantor set onto space. To this end use Burgess selection theorem. Finally, way assigning arc joining two selected points found.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2023
ISSN: ['1879-3207', '0166-8641']
DOI: https://doi.org/10.1016/j.topol.2023.108536