R^N的弱infinite dimensional子集
Weakly infinite dimensional subsets of R^N
摘要：
连续统假设意味着$\reals^{\naturals}$的第一范畴子集的理想和$\reals^{\naturals}$的可数维子集的理想之间的Erdös-Sierpienski对偶。$\reals^{\naturals}$的Hurewicz子集（Sierpinski集和Lusin集的维数理论类似物）与$\reals^{\naturals}$的任意紧可数维子集的代数和有第一范畴.
英文摘要：
The Continuum Hypothesis implies an Erdös-Sierpiński like duality between the ideal of first category subsets of $\reals^{\naturals}$, and the ideal of countable dimensional subsets of $\reals^{\naturals}$. The algebraic sum of a Hurewicz subset - a dimension theoretic analogue of Sierpinski sets and Lusin sets - of $\reals^{\naturals}$ with any compactly countable dimensional subset of $\reals^{\naturals}$ has first category.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
