Solve the question

[saptarshipatra107]

Let X = {a, b, c} be a set with three elements. Determine which of the following
collections are topologies on X.
(a) τ = {∅, X, {a}},
(b) τ = {∅, X, {a}, {a, b}},
(c) τ = {∅, X, {a}, {b, c}},
(d) τ = {∅, X, {a}, {b}, {c}}.

 

[topsquark]

How do you define what members are in a topology from a set? What members have to be there?

-Dan

 

[Deleted member 4993]

Let X = {a, b, c} be a set with three elements. Determine which of the following
collections are topologies on X.
(a) τ = {∅, X, {a}},
(b) τ = {∅, X, {a}, {a, b}},
(c) τ = {∅, X, {a}, {b, c}},
(d) τ = {∅, X, {a}, {b}, {c}}.

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[pka]

See Here
A topology on a set [imath]T[/imath] is a collection [imath]\tau[/imath] of subsets of [imath]T[/imath]:
that collection must contain [imath]T~\&~\emptyset[/imath] and be closed under union and finite intersection.