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**1. Homework Statement**

Ok I created this question to check my thinking.

Are the following Sets: Open, Closed, Compact, Connected

Note: Apologies for bad notation.

S: [0,1)∪(1,2]

V: [0,1)∩(1,2]

**2. Homework Equations**

S: [0,1)∪(1,2]

V: [0,1)∩(1,2]

**3. The Attempt at a Solution**

S: [0,1)∪(1,2]

Closed - because 0 and 2 represent boundary points

Compact - because S is closed and bounded

Not Connected - because it can be separated into two open disjoint sets [0,1) and [2]

V: [0,1)∩(1,2]

Open - because the set is (1)

Not Compact - because it is open

Connected - because it cannot be separated into two open disjoint sets