关于Peano连续统的Lusternik-Schnirelmann范畴
On the Lusternik-Schnirelmann category of Peano continua
摘要：
利用空间的一般子集覆盖定义LS-范畴cat_g，并证明了这个定义与紧度量ANR空间的经典Lusternik-Schnirelmann范畴是一致的.我们应用这个结果给出了Grossman-Whitehead定理和Dranishnikov定理的短维理论证明。我们计算了一些分形Peano连续统如Menger空间和Pontryagin曲面的cat_g。
英文摘要：
We define the LS-category cat_g by means of covers of a space by general subsets, and show that this definition coincides with the classical Lusternik-Schnirelmann category for compact metric ANR spaces. We apply this result to give short dimension theoretic proofs of the Grossman-Whitehead theorem and Dranishnikov's theorem. We compute cat_g for some fractal Peano continua such as Menger spaces and Pontryagin surfaces.
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