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In: Advanced Math

Which of the following sets is an abstract simplical complex? For each, if the answer is...

Which of the following sets is an abstract simplical complex? For each, if the answer is no, explain why; and if the answer is yes, give the dimension of the complex, and sketch its geometric realization, up to homeomorphism. a. {[a],[b],[a,b,c]},

b. {[a],[b],[c],[a,b,c]},

c. {[a],[b],[c],[a,b]},

d. {[a],[b],[c],[d],[a,b],[c,d]},

e. {[a],[b],[c],[d],[a,b],[b,c],[c,d],[a,d],[a,c],[a,b,c]}.

Solutions

Expert Solution

The answer is: Part (c) ,(d) and (e) are complexes. Explanation and geometric realizations are attached.

Colby Messinger answered 1 week ago
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