Mathematics Homework Solutions
Problem
#34069

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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question 4.doc
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.

Please give reasons with your answers.

Solution Summary

Topologies and open sets are investigated.

Solution
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