restart;
with(combinat):
#A procdure to find the extremal topologies and Non-Trivial Minimal Topologies;
#(1)A procedure to finid the finite set X;
pp:=proc(n)
local i;
{seq(x[i],i=1..n)};
end:
#ENTER THE NUMBER of ELEMENTS(POINTES);
n:=2;
X:=pp(n);
IiIj
PCQmSSJ4RzYiNiMiIiImRiQ2IyIiIw==
#(2) A procedure to generate extremal topology over X by x,y;
extremal:=proc(x,y,X)
local o,c,t,e,px,py,M,txy;
if `member`(x,X) and `member`(y,X) and x<>y then
c:={};M:={};txy:={};
px:=powerset(X minus {x});
for o in px do
if `member`(y,o) then
c:=c union {o};
else c:=c;
fi;
od;
c;
for e in c do
txy:=e union {x};
M:=M union {txy};
od;
px union M;
else flase;
fi;
end:
Generated_Extremal_Topology:=extremal(x[1],x[2],X);
print(`Numbers Of Open Setes is`,nops(Generated_Extremal_Topology));
PCU8IjwjJkkieEc2IjYjIiIjPCQmRiY2IyIiIkYl
NiRJOU51bWJlcnN+T2Z+T3Blbn5TZXRlc35pc0c2IiIiJA==
print(`Check if The Number of Open Sets is Identical with The Formula in 2-3 Theorem`,
evalb(nops(Generated_Extremal_Topology)=3*(2^(n-2))));
NiRJaG9DaGVja35pZn5UaGV+TnVtYmVyfm9mfk9wZW5+U2V0c35pc35JZGVudGljYWx+d2l0aH5UaGV+Rm9ybXVsYX5pbn4yLTN+VGhlb3JlbUc2IkkldHJ1ZUclKnByb3RlY3RlZEc=
#(3)A proceure to find all extremal topologies over a finite set X;
ALLExtremals:=proc(X)
local EX,x,y;
EX:={};
for x in X do
for y in X minus {x} do
EX:=EX union {extremal(x,y,X)};
od;
od;
EX;
end:
EXTREMALS:=ALLExtremals(X);
PCQ8JTwiPCMmSSJ4RzYiNiMiIiI8JEYmJkYnNiMiIiM8JUYkPCNGLEYr
print(`Number of Extremal Topologies is `,nops(EXTREMALS),`over a set with`,n,`points`);
NidJQk51bWJlcn5vZn5FeHRyZW1hbH5Ub3BvbG9naWVzfmlzfkc2IiIiI0kwb3Zlcn5hfnNldH53aXRoR0YkRiVJJ3BvaW50c0dGJA==
print(`Check if The Number of Extremal Topologies is Identical with Formula in Theorem 2-2 of [1]`,
evalb(nops(EXTREMALS)= n*(n-1)));
NiRJZXBDaGVja35pZn5UaGV+TnVtYmVyfm9mfkV4dHJlbWFsflRvcG9sb2dpZXN+aXN+SWRlbnRpY2FsfndpdGh+Rm9ybXVsYX5pbn5UaGVvcmVtfjItMn5vZn5bMV1HNiJJJXRydWVHJSpwcm90ZWN0ZWRH
#(4)A procedure to find the Non Trivial Minimal Topologies Over a Finite Set;
NTMT:=proc(X)
local o,c,PX,T;
c:={};T:={};
PX:=powerset(X);
for o in PX do
c:=c union{{{},o,X}};
od;
c minus {{{},X}};
end:
Non_Trivial_minimal_Topologies:=NTMT(X);
PCQ8JTwiPCMmSSJ4RzYiNiMiIiI8JEYmJkYnNiMiIiM8JUYkPCNGLEYr
The_Number_Of_Non_Trivial_Minimal_Topologies_is:=nops(NTMT(X));
IiIj
evalb(nops(NTMT(X))=(2^n)-2);
SSV0cnVlRyUqcHJvdGVjdGVkRw==
NiI=
n:=5;
IiIm
X:=pp(n);
PCcmSSJ4RzYiNiMiIiImRiQ2IyIiIyZGJDYjIiIkJkYkNiMiIiUmRiQ2IyIiJg==
Generated_Extremal_Topology:=extremal(x[2],x[3],X);
print(`Numbers Of Open Setes is`,nops(Generated_Extremal_Topology));
PDo8IjwjJkkieEc2IjYjIiIiPCMmRiY2IyIiJDwjJkYmNiMiIiU8IyZGJjYjIiImPCRGJUYrPCRGJUYvPCRGJUYzPCQmRiY2IyIiI0YrPCRGK0YvPCRGK0YzPCRGL0YzPCVGJUY6Ris8JUYlRitGLzwlRiVGK0YzPCVGJUYvRjM8JUY6RitGLzwlRjpGK0YzPCVGK0YvRjM8JkYlRjpGK0YvPCZGJUY6RitGMzwmRiVGK0YvRjM8JkY6RitGL0YzPCdGJUY6RitGL0Yz
NiRJOU51bWJlcnN+T2Z+T3Blbn5TZXRlc35pc0c2IiIjQw==
print(`Check if The Number of Open Sets is Identical with The Formula in Theorem 2-3 of [1]`,
evalb(nops(Generated_Extremal_Topology)=3*(2^(n-2))));
NiRJX3BDaGVja35pZn5UaGV+TnVtYmVyfm9mfk9wZW5+U2V0c35pc35JZGVudGljYWx+d2l0aH5UaGV+Rm9ybXVsYX5pbn5UaGVvcmVtfjItM35vZn5bMV1HNiJJJXRydWVHJSpwcm90ZWN0ZWRH
EXTREMALS:=ALLExtremals(X);
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
print(`Number of Extremal Topologies is `,nops(EXTREMALS),`over a set with`,n,`points`);
NidJQk51bWJlcn5vZn5FeHRyZW1hbH5Ub3BvbG9naWVzfmlzfkc2IiIjP0kwb3Zlcn5hfnNldH53aXRoR0YkIiImSSdwb2ludHNHRiQ=
print(`Check if The Number of Extremal Topologies is Identical with Formula in Theorem2-2 of [1]`,
evalb(nops(EXTREMALS)= n*(n-1)));
NiRJZHBDaGVja35pZn5UaGV+TnVtYmVyfm9mfkV4dHJlbWFsflRvcG9sb2dpZXN+aXN+SWRlbnRpY2FsfndpdGh+Rm9ybXVsYX5pbn5UaGVvcmVtMi0yfm9mflsxXUc2IkkldHJ1ZUclKnByb3RlY3RlZEc=
Non_Trivial_minimal_Topologies:=NTMT(X);
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
The_Number_Of_Non_Trivial_Minimal_Topologies_is:=nops(NTMT(X));
IiNJ
evalb(nops(NTMT(X))=(2^n)-2);
SSV0cnVlRyUqcHJvdGVjdGVkRw==
NiI=
n:=6;
IiIn
X:=pp(n);
PCgmSSJ4RzYiNiMiIiImRiQ2IyIiIyZGJDYjIiIkJkYkNiMiIiUmRiQ2IyIiJiZGJDYjIiIn
Generated_Extremal_Topology:=extremal(x[2],x[3],X);
print(`Numbers Of Open Setes is`,nops(Generated_Extremal_Topology));
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
NiRJOU51bWJlcnN+T2Z+T3Blbn5TZXRlc35pc0c2IiIjWw==
print(`Check if The Number of Open Sets is Identical with The Formula in Theorem 2-3 of [1]`,
evalb(nops(Generated_Extremal_Topology)=3*(2^(n-2))));
NiRJX3BDaGVja35pZn5UaGV+TnVtYmVyfm9mfk9wZW5+U2V0c35pc35JZGVudGljYWx+d2l0aH5UaGV+Rm9ybXVsYX5pbn5UaGVvcmVtfjItM35vZn5bMV1HNiJJJXRydWVHJSpwcm90ZWN0ZWRH
EXTREMALS:=ALLExtremals(X);
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
print(`Number of Extremal Topologies is `,nops(EXTREMALS),`over a set with`,n,`points`);
NidJQk51bWJlcn5vZn5FeHRyZW1hbH5Ub3BvbG9naWVzfmlzfkc2IiIjSUkwb3Zlcn5hfnNldH53aXRoR0YkIiInSSdwb2ludHNHRiQ=
print(`Check if The Number of Extremal Topologies is Identical with Formula in Theorem 2-2 of [1]`,
evalb(nops(EXTREMALS)= n*(n-1)));
NiRJZXBDaGVja35pZn5UaGV+TnVtYmVyfm9mfkV4dHJlbWFsflRvcG9sb2dpZXN+aXN+SWRlbnRpY2FsfndpdGh+Rm9ybXVsYX5pbn5UaGVvcmVtfjItMn5vZn5bMV1HNiJJJXRydWVHJSpwcm90ZWN0ZWRH
Non_Trivial_minimal_Topologies:=NTMT(X);
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
The_Number_Of_Non_Trivial_Minimal_Topologies_is:=nops(NTMT(X));
IiNp
evalb(nops(NTMT(X))=(2^n)-2);
SSV0cnVlRyUqcHJvdGVjdGVkRw==
JSFH
JSFH
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=