app core dumps!!

[jacek]

Because you add each item to the list twice:

...
layers_item[19]= new QListWidgetItem("Bookshops",layers); // <-- here
 
for (int i=0;i<=NumItems; i++){
   layers_item[i]->setCheckState(Qt::Unchecked);
   layers->addItem(layers_item[i]); // <-- and here
}

...
layers_item[19]= new QListWidgetItem("Bookshops",layers); // <-- here

for (int i=0;i<=NumItems; i++){
   layers_item[i]->setCheckState(Qt::Unchecked);
   layers->addItem(layers_item[i]); // <-- and here
}

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Remove the second line from that for loop and everything should be OK.