I am working with QGIS. I am creating a contour world map, I started my project with a raster image of the world and then extracted contour lines much too complex for my purposes. I simplified the polygons using a line generalization plugin. However I noticed that after simplifying some of my polygons are lapping into each other, how can I fix this.
You can do this using GRASS. According to this post: Generalizing polygon file while maintaining topology in QGIS?, GRASS will handle topology. So, before you generalize, set up topology and then use GRASS v.generalize to simplify the polygons.
However, as Michael Miles-Stimson pointed out, you are better off resampling your DEM at a lower resolution to create the generalize contours. This will be much more accurate that generalizing contours you have already produced.