Is a Topological Space T1, Regular or Normal

Suppose we have a setwith the topology

The closed sets are

Not every singleton set ofis closed since for examplehence the topology is not T1.

The topology is not closed andso the only open set containingis which also containsHenceis not regular.

The topological space is normal. Ifandare disjoint closed subsets ofthen one of them must beSupposethenand

Henceis normal.

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