The following functor retrieves the key set of a map:
#include <vector>
#include <iterator>
#include <algorithm>
template <class _Map>
std::vector<typename _Map::key_type> keyset(const _Map& map)
{
    std::vector<typename _Map::key_type> result;
    result.reserve(map.size());
    std::transform(map.cbegin(), map.cend(), std::back_inserter(result), [](typename _Map::const_reference kvpair) {
        return kvpair.first;
    });
    return result;
}
Bonus: The following functors retrieve the value set of a map:
#include <vector>
#include <iterator>
#include <algorithm>
#include <functional>
template <class _Map>
std::vector<typename _Map::mapped_type> valueset(const _Map& map)
{
    std::vector<typename _Map::mapped_type> result;
    result.reserve(map.size());
    std::transform(map.cbegin(), map.cend(), std::back_inserter(result), [](typename _Map::const_reference kvpair) {
        return kvpair.second;
    });
    return result;
}
template <class _Map>
std::vector<std::reference_wrapper<typename _Map::mapped_type>> valueset(_Map& map)
{
    std::vector<std::reference_wrapper<typename _Map::mapped_type>> result;
    result.reserve(map.size());
    std::transform(map.begin(), map.end(), std::back_inserter(result), [](typename _Map::reference kvpair) {
        return std::ref(kvpair.second);
    });
    return result;
}
Usage:
int main()
{
    std::map<int, double> map{
        {1, 9.0},
        {2, 9.9},
        {3, 9.99},
        {4, 9.999},
    };
    auto ks = keyset(map);
    auto vs = valueset(map);
    for (auto& k : ks) std::cout << k << '\n';
    std::cout << "------------------\n";
    for (auto& v : vs) std::cout << v << '\n';
    for (auto& v : vs) v += 100.0;
    std::cout << "------------------\n";
    for (auto& v : vs) std::cout << v << '\n';
    std::cout << "------------------\n";
    for (auto& [k, v] : map) std::cout << v << '\n';
    return 0;
}
Expected output:
1
2
3
4
------------------
9
9.9
9.99
9.999
------------------
109
109.9
109.99
109.999
------------------
109
109.9
109.99
109.999