How can I find nearest points in the same layer in ArcMap? I would like to find points that are in the distance of less then 0,5m.
Perhaps the easiest way is using the near tool if you have the license.
If you don't have the license then there are ways to code this functionality. Or you can possibly run a buffer of .5 m to create small polygons and then do a spatial join between the buffer and the point layers. Then you can select the points that share the same buffer feature ID.
You can create a 0.5m buffer zone and then use the select by location tool (top toolbar under Selection). At the target layer you select the buffer and at the source layer prompt the other layer. At the spatial selection method you can select "are within the source layer feature".
What about a buffer ? Does it works ? It's a better way to create that. You'll see all the points that you want.
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