I do not believe that question is for this forum, but I will try to participate with an answer anyway.
An extended use case is independent in itself. It is used to add or to extend the functionality of another use case, which in itself is complete, also.
For instance, let's say you have use case named place order and they ask you now that for clients that have bought more than 1.000 USD in the past sixth months before the new order you will grant them a rebate of 5% and send them an email notifiying them of this benefit.
This new behavior can be modeled as an extended use case. First, because your current use case "place order" is already complete, and this would simply be extending the behavior of the current use case. Without this new behavior the system would continue to work, and the use case "place order" still would offer business value to the user.
So, place order use case does not depend on grant benefits use case. It is and will continue to be indendepent of this behavior to work.
Nevertheless, the steps in the use case grant benefits depends on a condition (aka extension point) defined in the place order use case to be executed. That condition is: when you place an order and determine that client has bought more than 1000 USD in the previous sixth months.
Therefore, the gran benefits use case depends on the place order use case and not otherwise.
Do not try to undertand this from the coding point view, because if you created the class model for this, probably, this dependency cou,ld be modeled all the way round. [ October 23, 2006: Message edited by: Edwin Dalorzo ]
As long as the inheritance relationship is declared in such a way that RemoteObject is the one that extends from Object there is no problem with this diagram that you mention.
The appearance of "<extends>" seems to be the declaration of a stereotype to set a bit clearer that this is an inheritance case. Completely uneccesary, I daresay, since UML notation already sets that clear, but yet valid.
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