Local and global \(\sigma\)-cone porosity. (English) Zbl 0816.46014

Holický, P.

Acta Univ. Carol., Math. Phys. 34, No. 2, 51-57 (1993).

Summary: We compare two subclasses of first category sets in Hilbert spaces, one of \(\sigma-\alpha\)-cone porous and the other of \(\sigma- \alpha\)-angle porous sets. Our Theorem gives a positive result whence an example shows that these two notions do not coincide.

MSC:

46C05

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

Keywords:

\(\sigma\)-cone porosity; subclasses of first category sets in Hilbert spaces; porous sets