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Topologies : Open Sets

? Let X:={a,b,c} be a set of three elements. A certain topology of X contains (among others) the sets {a}, {b}, and {c}. List all open sets in the topology T.
? Let X':={a,b,c,d,e} be a set of five elements. A certain topology T' on X' contains (among others) the sets {a,b,c}, {c,d} and {e}. List any other open set in T' which you know must be there. Also name one subset of X' which may or may not be open.

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1. X={a,b,c}, the topology T contains {a}, {b}, {c}, then any subset of X is an open set in T.
T={empty set, X, {a}, {b}, {c}, ...

Solution Summary

Topologies and open sets are investigated.