$$o2 @l $$c ,9troduc;n $p ,a topological space is sd 6be p>a-,l9del( if e op5 cov] ( x has a loc,y c.ta# op5 ref9e;t4 ,! subject ( loc,y f9ite collec;ns ( op5 sets & p>acompact spaces has be5 fairly well develop$ = "s "t4 ,h["e1 ! "u/&+ ( _! w1k] c.t]"ps1 loc,y c.ta# collec;ns ( op5 sets & p>a-,l9del( spaces1 is relatively sket*y4 ,! develop;ts 9 ? >ea ^u : ? pap] builds1 due ma9ly 6,fleissn] & ,re$ & al ext5d$ 0,burke1 >e r rec5t4 ,! ma9 "q answ]$ 9 ? pap]1 ask$ 0,f$orcuk ,7#aj7'1 ,tall ,7#ad7'1 ,fleissn] ,7#a7'1 ,re$ ,7#b7'1 ,burke ,7#e7'1 & ,nyikos ,7#f7'1 is3 ,m/ e p>a-,l9del( @m ,t3-space @l 2 p>acompact8 ,! answ] is no 7n ev5 -pletely regul> or metacompact71 z we w demon/rate )a v>iety ( examples4 $p ,p>a-,l9del( spaces m/ 2 assum$ 6be @m ,t3 @l 6provide an 9t]/+ !ory1 = "! is a space )a c.ta# basis : is ,hausdorf b n regul>4 ,on ! o!r h&1 p>compact;s ri*ly 5d[s @m ,t2-spaces with all of the below separation properties, connected in @m ,t1-spaces @l 0! 9 ! 9dicat$ implic,ns3 $l $$ub ,hausdorff $$uf @m $[33 @l $$ub regul> $$uf @m $[33 @l $$ub -pletely regul> $$uf @m $[33 @l $$ub normal $$uf @m $l $$p5 $a-,l9del( @m ,t3-spaces @l >e collec;nwise ,hausdorf1 9 fact /r;gly s1 & >e ?us ( 9t]e/ 6^? /udy+ ! normal ,moore space pro#m4 ,9clud$ am;g ! spaces we w 3/ruct >e p>a-,l9del( @m ,t1-spaces @l : >e respectively regul> b n -pletely regul>1 -pletely regul> b n normal1 & normal b n collec;nwise normal4 ,we w al 3sid] "s (! o!r cov]+ prop]ties 5joy$ 0p>acompact @m ,t2-spaces_1 @l s* z c.ta# p>acompact;s1 metacompact;s1 & scre5abil;y4 $p ,9 ,*apt] #b "! is a brief review ( "s (! basic facts reg>d+ p>a-,l9del( spaces4 ,*apt] #c 4cusses ! te*niques us$ 9 ! se>* =a p>a-,l9del(1 nonp>acompact @m ,t3-space_1 @l due ma9ly 6,fleissn] ,7#a7'4 ,? pap]'s ma9 examples ( s* spaces >e pres5t$ 9 ,*apt]s #d & #e4 ,9 ,*apt] #f ! 9=m,n ga9$ f ^! examples is amplifi$1 & "s relat$ unansw]$ rese>* "qs >e ask$4