*Definition [#i38519bf]
-A subset &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20S%5csubset%20X%20%5c%5d%7d%25.png); is an open filter adherence if &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20S=ad%5cmathcal%7bF%7d:=%5ccap_%7bF%5cin%5cmathcal%7bF%7d%7dcl%20F%20%5c%5d%7d%25.png); for some open filter &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cmathcal%7bF%7d%20%5c%5d%7d%25.png);  on X .

*Reference [#r479ac83]
-Krystock, Robert L., ''Adherent compact spaces. (English)'', Proc. Am. Math. Soc. 107, No.4, 1117-1125 (1989).