Answered Same DayApr 05, 2022


Rajeswari answered on Apr 05 2022
9 Votes
103318 assignment
We can see that only is W is complete the pointwise limit lies in W for all elements.(see part ii of the proof where we used Tn tends to T)
Otherwise this proof is not valid.
Hence we can conclude that if W is not complete binary operation from V to W also would not be complete.
1. Let K be the union of all subsets K1, K2…Kn
It follows that K is compact.
i.e. union of K1, K2…Kn is also compact set if each Ki is compact
2. Here we are to prove that if n is infinite i.e. when n becomes abnormally large the union may not be compact.
Consider the step
When n becomes very large G0 cannot be an open cover for K.
Hence union need not be compact
Note: Please note that I used T here instead of f as I assumed T is the mapping.
This will not affect the proof
We have, a subalge
a is a subset of an alge
a, closed under all its operations, and ca
ying the induced operations.

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