spatial data finding points within a radius of other points

I have some lon & lat data. I would like to create new variables/columns based on the spatial features. That is for each point P I want to set a perimeter around it and group all other points within that perimeter. Say Pa and Pc might be neighbours of Pb but Pa and Pc might not be neighbours of each other. I am developing a model which will use data from points which are closer to point Pa and ignore data which is far away from point Pa, and then a different model will also be built which will use points Pc and only consider data close to Pc.

         lon      lat            offense
1  -95.46866 29.87108           burglary
2  -95.31358 29.93452            robbery
3  -95.24957 29.86051           burglary
4  -95.59642 29.67272           burglary
5  -95.30692 30.00263              theft
6  -95.39709 29.70991         auto theft
7  -95.29878 29.73458              theft
8  -95.49082 29.69905              theft
9  -95.37682 29.81252         auto theft

Data:

    library(ggmap)

df <- crime %>% 
  sample_n(20) %>% 
  select(lon, lat, offense)


houston <- get_map("houston, texas")

ggmap(houston) +
  geom_point(data = df, aes(x = lon, y = lat, alpha = 0.5))

P is trasitive if xPb and bPc, then; aPc.