Matematické Fórum

Ulohou bolo najst vsetky topologie na trojprvkovej mnozine a urcite, ktore su najvzajom homeomorfne. Vypisane ich mam vsetky spravne, len by som chcela vediet, ci mam spravne aj urcenie tych homeomorfnych, dakujem :)

X = {a,b,c}

T1  = {PM, X}
T2  = {PM, X, {a}, {b}, {c}, {a;b}, {a;c}, {b;c}}
T3  = {PM, X, {a}}
T4  = {PM, X, {b}}
T5  = {PM, X, {c}}
T6  = {PM, X, {a;b}}
T7  = {PM, X, {a;c}}
T8  = {PM, X, {b;c}}
T9  = {PM, X, {a}, {a;b}, {a;c}}
T10 = {PM, X, {b}, {a;b}, {b;c}}
T11 = {PM, X, {c}, {a;c}, {b;c}}
T12 = {PM, X, {a}, {a;b}}
T13 = {PM, X, {a}, {a;c}}
T14 = {PM, X, {b}, {b;c}}
T15 = {PM, X, {b}, {a;b}}
T16 = {PM, X, {c}, {a;c}}
T17 = {PM, X, {c}, {b;c}}
T18 = {PM, X, {a}, {b;c}}
T19 = {PM, X, {b}, {a;c}}
T20 = {PM, X, {c}, {a;b}}
T21 = {PM, X, {a}, {b}, {a;b}}
T22 = {PM, X, {a}, {c}, {a;c}}
T23 = {PM, X, {b}, {c}, {b;c}}
T24 = {PM, X, {a}, {b}, {a;b}, {a;c}}
T25 = {PM, X, {a}, {b}, {a;b}, {b;c}}
T26 = {PM, X, {a}, {c}, {a;c}, {b;c}}
T27 = {PM, X, {a}, {c}, {a;c}, {a;b}}
T28 = {PM, X, {b}, {c}, {b;c}. {a;c}}
T29 = {PM, X, {b}, {c}, {b;c}, {a;b}}

homeomorfne:
T3, T4, T5
T6, T7, T8
T9, T10, T11
T12 - T17
T18 - T20
T21, T22, T23
T24 - T29