C ∗ ( E ) is (topologically) simple.
By [57, p. 215], for any unital C ∗ -algebra A, A is topologically simple if and only if A is algebraically simple.
By [47, Proposition 5.1] (for the case without sources), and [86] (for the general case), C ∗ ( E ) is (topologically) simple if and only if E is cofinal and has Condition (L).
On the other hand if the completion ({widehat{L}}(Gamma )) is topologically graded simple then it is topologically graded prime.
By Theorem 2 the completion ({widehat{L}}(Gamma )=I(W_1)) is topologically graded simple.
If (gamma ) is a regular specialization then the Leavitt path algebra (L(Gamma )) is prime if and only if the completion ({widehat{L}}(Gamma )) is topologically graded simple.
Fractional quantum Hall (FQH) states are topologically ordered.
The idea is that, say, all tube tops are topologically equivalent — they all have the same number of holes.
On another hand, halter tops and men's trunks are topologically equivalent (go ahead, try stretching one into the other).
The resulting numbers are called Betti numbers, and structures with the same Betti numbers are topologically equivalent.
This implies that all these examples are topologically -nullbordant.
