*Definition [#eafca25c]
A pseudometric space is said to be Heine-Borel-compact if every open cover has a finite subcover.
*Remark [#vfe09b72]
-See [[compact]].

*Reference [#j8aae093]
Horst Herrlich, ''Choice principles in elementary toplogy and analysis'', Comment. Math. Univ. Carolinae 38,3(1997) 545-552.