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C-compact

Last-modified: 2010-12-26 (日) 12:18:49

Definition 1 Edit

A topological space is said to be C-compact (abbreviated as CC) if every closed set is an H-set.

Definition 2 Edit

For subspaces of topological spaces, C-compactness is the same as C_ω-compactness. Here ω denotes countable cardinality.

Definition 3 Edit

A topological space is called c-compact if for every topological space Y and every subset imgtex.fcgi?%5bres=100%5d%7b$S%5csubset%20X%5ctimes%20Y$%7d%25.png, imgtex.fcgi?%5bres=100%5d%7b$p_Y%28%5cmathrm%7bcl%7d_%7bX%5ctimes%20Y%7dS%29%5csubset%20cl_Yp_Y%28S%29$%7d%25.png, where imgtex.fcgi?%5bres=100%5d%7b$p_Y$%7d%25.png is the second projection imgtex.fcgi?%5bres=100%5d%7b$p_Y:X%5ctimes%20Y%5cto%20Y$%7d%25.png.

Remark Edit

Definition 1
  • G. Viglino, C-compact spaces. Duke Math. J., 36, 761-764 (1969).
  • R.F. Dickman, Jr. and J.R. Porter, Between minimal Hausdorff and compact Hausdorff spaces, Topology Proc. Vol.9 (1984), p.243-268.
Definition 2
Manuel Sanchis, Angel Tamariz-Mascarua, p-pseudocompactness and related topics in topological spaces, Topology and its Applications 98 (1999) 323-343.
Definition 3
C. M. Neira, The Kuratowski-Mrowka characterization and weak forms of compactness, Revista Colombiana de Matematicas Volumen 43(2009)1, paginas 9-17