Misleading compiler error message: size_t is not a member of std?

I have the following header file containing a template class:

#ifndef VECTOR_H
#define VECTOR_H

namespace lgl
{
    namespace maths
    {
        template<class T, std::size_t SIZE>
        class Vector
        {
        public:
            Vector();
            Vector(T defaultValue);
            Vector(const Vector<T, SIZE>& other);
            Vector<T, SIZE>& operator=(const Vector<T, SIZE>& other);
            ~Vector();

            //accessors
            const std::size_t size() const;
            const T& operator[](std::size_t i) const;
            T& operator[](std::size_t i);

            //vector operations
            Vector<T, SIZE> operator+(const Vector<T, SIZE>& other) const;
            Vector<T, SIZE> operator-(const Vector<T, SIZE>& other) const;
            Vector<T, SIZE> operator*(const T& scalar) const ;
            Vector<T, SIZE> operator/(const T& scalar) const ;
            T operator*(const Vector<T, SIZE>& other) const;

            void operator+=(const Vector<T, SIZE>& other);
            void operator-=(const Vector<T, SIZE>& other);
            void operator*=(const T& scalar);
            void operator/=(const T& scalar);

            bool operator==(const Vector<T, SIZE>& other) const;
            bool operator!=(const Vector<T, SIZE>& other) const;

        private:
            T m_elements[SIZE];

        };

        template<class T, std::size_t SIZE>
        std::ostream& operator<<(std::ostream& os, const Vector<T, SIZE>& vec);

        template<class T>
        Vector<T, 3> cross(const Vector<T, 3>& a, const Vector<T, 3>& b);

        #include "Vector.tpp"

        //typedefs
        typedef Vector<float, 2> vec2f;
        typedef Vector<float, 3> vec3f;
        typedef Vector<float, 4> vec4f;
        typedef Vector<double, 2> vec2d;
        typedef Vector<double, 3> vec3d;
        typedef Vector<double, 4> vec4d;
        typedef Vector<int, 2> vec2i;
        typedef Vector<int, 3> vec3i;
        typedef Vector<int, 4> vec4i;

        //factories
        vec2f getVec2f(float x, float y);
        vec3f getVec3f(float x, float y, float z);
        vec4f getVec4f(float x, float y, float z, float h);
    }
}

#endif

The .tpp file has all the implementations of the methods of the Vector template class. I also have a Vector.cpp file, which defines the factory functions, like this:

#include "Vector.h"

namespace lgl
{
    namespace maths
    {
        //factories
        vec2f getVec2f(float x, float y)
        {
            vec2f result;
            result[0] = x;
            result[1] = y;
            return result;
        }

        vec3f getVec3f(float x, float y, float z)
        {
            vec3f result;
            result[0] = x;
            result[1] = y;
            result[2] = z;
            return result;
        }

        vec4f getVec4f(float x, float y, float z, float h)
        {
            vec4f result;
            result[0] = x;
            result[1] = y;
            result[2] = z;
            result[3] = h;
            return result;
        }
    }
}

I get the errors: size_t is not a member of std, and ostream is not a member of std. If I delete everything in the .cpp file and don't use the factories, everything's fine. So what could be the problem?