With Swift 5.1, you can use one of the three following examples in order to solve your problem.
#1. Using Array's map(_:) method and Set's init(_:) initializer
In the simplest case, you can map you initial array to an array of urls (String) then create a set from that array. The Playground below code shows how to do it:
struct MyObject {
    let url: String
}
let objectArray = [
    MyObject(url: "mozilla.org"),
    MyObject(url: "gnu.org"),
    MyObject(url: "git-scm.com")
]
let urlArray = objectArray.map({ $0.url })
let urlSet = Set(urlArray)
dump(urlSet)
// ▿ 3 members
//   - "git-scm.com"
//   - "mozilla.org"
//   - "gnu.org"
struct MyObject {
    let url: String
}
let objectArray = [
    MyObject(url: "mozilla.org"),
    MyObject(url: "gnu.org"),
    MyObject(url: "git-scm.com")
]
let urlSet = objectArray.reduce(into: Set<String>(), { (urls, object) in
    urls.insert(object.url)
})
dump(urlSet)
// ▿ 3 members
//   - "git-scm.com"
//   - "mozilla.org"
//   - "gnu.org"
As an alternative, you can use Array's reduce(_:_:) method:
struct MyObject {
    let url: String
}
let objectArray = [
    MyObject(url: "mozilla.org"),
    MyObject(url: "gnu.org"),
    MyObject(url: "git-scm.com")
]
let urlSet = objectArray.reduce(Set<String>(), { (partialSet, object) in
    var urls = partialSet
    urls.insert(object.url)
    return urls
})
dump(urlSet)
// ▿ 3 members
//   - "git-scm.com"
//   - "mozilla.org"
//   - "gnu.org"
#3. Using an Array extension
If necessary, you can create a mapToSet method for Array that takes a transform closure parameter and returns a Set. The Playground below code shows how to use it:
extension Array {
    func mapToSet<T: Hashable>(_ transform: (Element) -> T) -> Set<T> {
        var result = Set<T>()
        for item in self {
            result.insert(transform(item))
        }
        return result
    }
}
struct MyObject {
    let url: String
}
let objectArray = [
    MyObject(url: "mozilla.org"),
    MyObject(url: "gnu.org"),
    MyObject(url: "git-scm.com")
]
let urlSet = objectArray.mapToSet({ $0.url })
dump(urlSet)
// ▿ 3 members
//   - "git-scm.com"
//   - "mozilla.org"
//   - "gnu.org"