Floating point keys in std:map

The following code is supposed to find the key 3.0in a std::map which exists. But due to floating point precision it won't be found.

map<double, double> mymap;
mymap[3.0] = 1.0;

double t = 0.0;
for(int i = 0; i < 31; i++)
{
  t += 0.1;
  bool contains = (mymap.count(t) > 0);
}

In the above example, contains will always be false. My current workaround is just multiply t by 0.1 instead of adding 0.1, like this:

for(int i = 0; i < 31; i++)
{
  t = 0.1 * i;
  bool contains = (mymap.count(t) > 0);
}

Now the question:

Is there a way to introduce a fuzzyCompare to the std::map if I use double keys? The common solution for floating point number comparison is usually something like a-b < epsilon. But I don't see a straightforward way to do this with std::map. Do I really have to encapsulate the double type in a class and overwrite operator<(...) to implement this functionality?