Solve the question

saptarshipatra107

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

-Dan
 
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}}.
Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.
 
See Here
A topology on a set TT is a collection τ\tau of subsets of TT:
that collection must contain T & T~\&~\emptyset and be closed under union and finite intersection.
 
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