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Short answer yes.
All the named varieties of apples started out as a single plant and sometimes a single branch. From there they were propagated by grafting cuttings called scions onto another apple. There are several series of root stocks that have been developed to give various size trees plus other characteristics.
One of the first series developed is the Malling series bred at the East Malling Research station in East Malling England, There is the Budagovsky series from the Soviet union. There are others. A breeding program in Ottawa. Others were developed in VIneland, Ontario. A a series from Geneva, NY.
There is another factor. Apples need a period of cold weather to grow and fruit. I don't know if they will even stay alive in Singapore.
Apples are very highly bred; I believe I've heard that only one out of ten thousand seedlings is as good as its parent, and one out of a hundred thousand surpasses it. Don't let that stop you from trying, though! You might hit the lottery. :-)
Apples require cold weather to trigger them to flower, but it's actually possible to fool them into thinking that winter has arrived and thereby getting a crop even in tropical conditions. There's a description of the process here. http://www.tradewindsfruit.com/apple.htm . Basically, you stop watering it and pull off all the leaves, fooling it into thinking that winter has arrived and it needs to go dormant.
I'd imagine your best chance of success, if you want to try a tree in Singapore, would be to choose the seeds of a subtropical variety with a low chill requirement.