- #1

Carl140

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## Homework Statement

Let X be a topological space, a subset S of X is said to be locally closed if

S is the intersection of an open set and a closed set, i.e

S= O intersection C where O is an open set in X and C is a closed set in X

Prove that if M,N are locally closed subsets then M union N is locally closed.

## The Attempt at a Solution

So M = O intersection C and N = O' intersection C' where O, O' are open sets in X and

C, C' are closed sets in X.

It follows that M union N = (O intersection C) U (0' intersection C').

From h ere I played with this expression a while using distributive laws but got stuck,

somewhere I end up with the union of a closed set and an open set, i.e O U C, but I think

we cannot said anything about this particular union. Maybe I'm missing some useful

set-theoretical identity. Can you please help?