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"

#2. Using Array's reduce(into:_:) 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(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"

In the simplest case, with Swift 3, you can use Array's init(_:) initializer to get an Array from a Set. init(_:) has the following declaration:

init<S>(_ s: S) where S : Sequence, Element == S.Iterator.Element

Creates an array containing the elements of a sequence.

Usage:

let stringSet = Set(arrayLiteral: "car", "boat", "car", "bike", "toy")    
let stringArray = Array(stringSet)

print(stringArray)
// may print ["toy", "car", "bike", "boat"]

However, if you also want to perform some operations on each element of your Set while transforming it into an Array, you can use map, flatMap, sort, filter and other functional methods provided by Collection protocol:

let stringSet = Set(["car", "boat", "bike", "toy"])
let stringArray = stringSet.sorted()

print(stringArray)
// will print ["bike", "boat", "car", "toy"]

let stringSet = Set(arrayLiteral: "car", "boat", "car", "bike", "toy") 
let stringArray = stringSet.filter { $0.characters.first != "b" }

print(stringArray)
// may print ["car", "toy"]

let intSet = Set([1, 3, 5, 2]) 
let stringArray = intSet.flatMap { String($0) }

print(stringArray)
// may print ["5", "2", "3", "1"]

let intSet = Set([1, 3, 5, 2])
// alternative to `let intArray = Array(intSet)`
let intArray = intSet.map { $0 }

print(intArray)
// may print [5, 2, 3, 1]