*Definition 1 [#ldeb8e7d]
A topological space is said to be C-compact (abbreviated as CC) if every closed set is an [[H-set]].

*Definition 2 [#d3f355f0]
For subspaces of topological spaces, C-compactness is the same as [[C_ω-compactness>C_α-compact]]. Here ω denotes countable cardinality.

*Definition 3 [#oea9b0b3]
A topological space is called c-compact if for every topological space Y and every subset &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$S%5csubset%20X%5ctimes%20Y$%7d%25.png);, &ref(http://www.eaflux.com/imgtex/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 &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$p_Y$%7d%25.png); is the second projection &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$p_Y:X%5ctimes%20Y%5cto%20Y$%7d%25.png);.
*Remark [#pbd69e9f]
: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