- #1

MathematicalPhysicist

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Let Y be a subset of X, and X and Y are connected, show that if A and B form a separation of X-Y then YUA and YUB are connected.

Attempt at solution:

Well I'm not sure where the fact that X is connected comes to play (perhaps it gurantees us the possibility of X-Y not to be connected).

anyway if we look at: seperations of YUB=CUD and YUA=C'UD'

then Y=(YUB)-B=(C-B)U(D-B), Y=(YUA)-A=(C'-A)U(D'-A)

which are both seperations of Y which is a contradiction to Y being connected, am I correct here or yet again wrong?

any input?

thanks in advance.