Mazurkiewicz–Sierpiński paradox

Target entity: Mazurkiewicz–Sierpiński paradox
Context triple: [Stefan Mazurkiewicz, notableWork, Mazurkiewicz–Sierpiński paradox]

• A. Banach–Tarski paradox
  The Banach–Tarski paradox is a theorem in set-theoretic geometry stating that a solid ball in 3‑dimensional space can be decomposed into finitely many non-measurable pieces and reassembled into two identical copies of the original ball, highlighting counterintuitive consequences of the axiom of choice.
• B. Mazurkiewicz–Sierpiński theorem
  The Mazurkiewicz–Sierpiński theorem is a result in topology and measure theory that characterizes certain properties of measurable sets and mappings, particularly concerning continuous images of sets in Euclidean spaces.
• C. Sierpiński set
  The Sierpiński set is a subset of the real numbers with the property that it intersects every uncountable closed subset of the reals in only countably many points, illustrating extreme pathological behavior in set theory and real analysis.
• D. Banach–Mazur game
  The Banach–Mazur game is an infinite two-player topological game used to characterize properties such as Baire category and completeness in metric and topological spaces.
• E. Steinhaus theorem
  The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Mazurkiewicz–Sierpiński paradox
Target entity description: The Mazurkiewicz–Sierpiński paradox is a result in set-theoretic geometry showing that a sphere can be decomposed and reassembled in a counterintuitive way, illustrating the existence of paradoxical decompositions similar to the Banach–Tarski paradox.

• A. Banach–Tarski paradox
  The Banach–Tarski paradox is a theorem in set-theoretic geometry stating that a solid ball in 3‑dimensional space can be decomposed into finitely many non-measurable pieces and reassembled into two identical copies of the original ball, highlighting counterintuitive consequences of the axiom of choice.
• B. Mazurkiewicz–Sierpiński theorem
  The Mazurkiewicz–Sierpiński theorem is a result in topology and measure theory that characterizes certain properties of measurable sets and mappings, particularly concerning continuous images of sets in Euclidean spaces.
• C. Sierpiński set
  The Sierpiński set is a subset of the real numbers with the property that it intersects every uncountable closed subset of the reals in only countably many points, illustrating extreme pathological behavior in set theory and real analysis.
• D. Banach–Mazur game
  The Banach–Mazur game is an infinite two-player topological game used to characterize properties such as Baire category and completeness in metric and topological spaces.
• E. Steinhaus theorem
  The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
• F. None of above. chosen