实函数间断点的某些特性

511995Vol.5N0.1OURNALOFJINANUNIVERSITY,;;;1.1,,,,,E(,b)E{x,}lC,}1Cf(x)C,,x,x,:,x~1x,,f(x)(a,b),f(x)(a,b),f(x)(a,b)2.2f(x)[a,;(x),,(x):(l):[c.+a(aO)(2)(:,+(x)(3)hmf()k.+f(x).k.():,Oxa,:f()f()x:+x(l)xO:(c+)((l)limf,()limf,()~k.+~,2,,b,(x),(x):,(),():,().(x).2a.f(x)I.)If(x)I}{},O_____,_.,,,~~~,:f({i:(983.,11f()f()f()f(x)f()3.3f(:f)4._(.:::)_:)_:+)~_)_)::1(:(f).:(;.).,.:).P::.1)_)_:)2t)P),r/)_P:.1..:)_:+.1);:).}m_:...(;...g:._,).;;.(:,::(,.).,).:::f(x,)Pf()(2)aqtx,f(t)P(3);:rbf)P(4)f(:)P(x:)(5)qx:f(:)P(:trbf(t)p(7),x:x,xZ,q,:b,x,tx:.(3)f(t)P,(5)f(t)P,::.f(x)f()E::E3~(xlf(x)~f(x+)f(.x(ab)}:,(a.b)}hmf(t)(x)lx,.:1XZ,:(,)()(X)f(tf(x:).,.()(*~1,2,){x},x(k+2~~2-~~_,/.1;,l,,.,,;,It!}x{{}}xi))hmf(:,*)limf(*)lirnf(,):o,}Iimf(:)f(x)l:~txE:E3hmf(t)f(x)x(a.b)N,N_.,.,,,,,1,.,,,,~1,}(j(t)j(x)}{xll(j(t)f()Ix(a)}N+2E,E3c,4E,.E3+l[WRudin,,..,1979SOMEPROPERTIESOFREALFUNCTIONDISCONTINUITYPOINTHanZhenlai(DepartmentofMathematies)AbstraetThispapergivessomeproperriesofseveralspeeialfunetiondiseontinuitypointandthefirstkinddiseontinuityPointofordinaryrealfunetion.andpointsoutrheirap-plieaioninaetualProblems.Keyrdsdiseontinuitrpoin:ofthefirstkind;diseon:inui:),pointoftheseeondkind;eountable;monotone