Error mismatch between String and [String: String] in case statement in switch code

I got stuck on this after trying different ways to pull out the information from the dictionary into the case part. The error said that one part is a String and the other [String:String], but I thought that when I write world["BEL"], this should only give out the string "Brussels", so I'm confused about which parts don't match.

Also, I tried to put all the remaining capitals into one switch statement, but can't figure out what to put to avoid having to write out the code for each capital. I tried

default: otherCapitals.append(world[value])

because I thought this would put only the value from the dictionary from whichever other capital there was, but this only gave me an error.

var europeanCapitals: [String] = []
var asianCapitals: [String] = []
var otherCapitals: [String] = []

let world = [
  "BEL": "Brussels", 
  "LIE": "Vaduz", 
  "BGR": "Sofia", 
  "USA": "Washington D.C.", 
  "MEX": "Mexico City", 
  "BRA": "Brasilia", 
  "IND": "New Delhi", 
  "VNM": "Hanoi"]

for (key, value) in world {

    switch world {

    case world["BEL"]: europeanCapitals.append("Brussels")
    case "LIE": europeanCapitals.append("Vaduz")
    case "BGR": europeanCapitals.append("Sofia")
    case "VNM": asianCapitals.append("Hanoi")
    default: otherCapitals.append("IDK")

    }
}