Ole Thompson and Caroline Olsen traveled to the USA very soon after their marriage in Norway in 1881. There are some hints that they may have initially been in Southern Minnesota or Sioux Falls, SD, before finally moving to Potter County, SD. (Some of Ole's sisters settled in the vicinity of southeastern MN.) In Norwegian records Ole and Caroline were known as Ole Thorsen Rundhaugen and Caroline Olsdatter Bratasvedjan. How they arrived at the surname Thompson is a mystery to me.
A family group form for their family is included here. Ahnetafel (ancestry) reports for each are here. A fan type of pedigree chart centered on one of their children is here. A more traditional interactive pedigree chart centered on one of their children is here. I have also assembled more detailed information in an attachment that includes source descriptions and photos.
Their places of origin in Norway are roughly shown in blue in the old map that follows. Caroline was from the Trondheim area near the north part of the map. Following the map is a picture taken about 1910 of the family. The person to Caroline's right is her nephew, Ed Olsen, who I now understand settled not too far from Billings, MT. The picture hanging in the background is their deceased daughter, Anna.