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From Wikipedia, sixteen T₀ topologies on a four-set —

{∅, {a}, {a, b}, {a, b, c}, {a, b, d}, {a, b, c, d}} (T₀)

{∅, {a}, {a, b}, {a, c}, {a, b, c}, {a, b, c, d}} (T₀)

{∅, {a}, {b}, {a, b}, {a, c}, {a, b, c}, {a, b, c, d}} (T₀)

{∅, {a}, {a, b}, {a, b, c}, {a, b, c, d}} (T₀)

{∅, {a}, {b}, {a, b}, {a, b, c}, {a, b, c, d}} (T₀)

{∅, {a}, {a, b}, {c}, {a, c}, {a, b, c}, {a, b, d}, {a, b, c, d}} (T₀)

{∅, {a}, {a, b}, {a, c}, {a, b, c}, {a, b, d}, {a, b, c, d}} (T₀)

{∅, {a}, {b}, {a, b}, {a, b, c}, {a, b, d}, {a, b, c, d}} (T₀)

{∅, {a}, {b}, {a, b}, {a, c}, {a, b, c}, {a, b, d}, {a, b, c, d}} (T₀)

{∅, {a}, {b}, {a, b}, {b, c}, {a, b, c}, {a, d}, {a, b, d}, {a, b, c, d}} (T₀)

{∅, {a}, {a, b}, {a, c}, {a, b, c}, {a, d}, {a, b, d}, {a, c, d}, {a, b, c, d}} (T₀)

{∅, {a}, {b}, {a, b}, {a, c}, {a, b, c}, {a, d}, {a, b, d}, {a, c, d}, {a, b, c, d}} (T₀)

{∅, {a}, {b}, {a, b}, {c}, {a, c}, {b, c}, {a, b, c}, {a, b, d}, {a, b, c, d}} (T₀)

{∅, {a}, {b}, {a, b}, {c}, {a, c}, {b, c}, {a, b, c}, {a, d}, {a, b, d}, {a, c, d}, {a, b, c, d}} (T₀)

{∅, {a}, {b}, {a, b}, {c}, {a, c}, {b, c}, {a, b, c}, {a, b, c, d}} (T₀)

{∅, {a}, {b}, {a, b}, {c}, {a, c}, {b, c}, {a, b, c}, {d}, {a, d}, {b, d}, {a, b, d}, {c, d}, {a, c, d}, {b, c, d}, {a, b, c, d}} (T₀)

Compare and contrast with the finite geometry  of the power set of a four-set.