On the Lusternik-Schnirelmann category of Peano continuaReport as inadecuate



 On the Lusternik-Schnirelmann category of Peano continua


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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 Dranishnikovs theorem. We compute cat g for some fractal Peano continua such as Menger spaces and Pontryagin surfaces.



Author: Tulsi Srinivasan

Source: https://archive.org/



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