Definition Of The Complement Of A Set

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Hello, my book defines the complement of a set like so: {x ∈ U | x /∈ A}

To me, it seems like the definition should be (x| x \in U \wedge x \notin A)

Which is more proper?
 
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They both say exactly the same thing.
 
Okay, thank you.
 

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A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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