I am afraid that there is not a solution (not everything is possible!).
But I want to have the satisfaction of being able to explain what I mean
When I show the list via the ShowDropDown command and the user selects an item, this item "passes" into the AutoCompleteEditText.Text, then the list closes.
Reopening the list, it shows all items, not just those that begin with the same characters (ie not only the selected "Edit" and "EditText" but all the items) and this is the correct behavior.
Instead, when I write in the code: AutoCompleteEditText.Text = "Edit" because the user has added the item "Edit" (by pressing the Add button (+)), at that point, opening the list again using the command ShowDropDown, the list will only display the "Edit" and "EditText".
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One way to overcome this would be the use of a Listview, as in your class. But in your class SearchView you use AddToParent to "create" the view, getting the Parent object (Activity or Panel) from it.
I will not be able to add a Listview because the custom view must be adapted for the designer, and then I will not have the Parent object.
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I searched for a way to get the "container" for a view.
I found
this but I do not know if it is possible to do something via Reflection.
Thanks again for your help, Erel.