*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.