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This question already has an answer here:

I'm converting a raster data to vector data.

The problem is similar to this: How to smooth large vector polygons from Raster

But what I need to know is how can I handle out the gaps that are formed between the polygons?

I want the gaps to be filled with the polygon near to it.

marked as duplicate by underdark qgis Jun 7 '17 at 16:33

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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