This paper presents an online topological mapping method on a quadcopter with fast-growing neural gas. Recently, perceiving the real world in 3D space has become increasingly important, and robotics is no exception. Quadcopters are the most common type of robot working in 3D space. The ability to perceive 3D space is even required in order to enable real-time autonomous control. Dense maps are simply unpractical, while sparse maps are not suitable due to a lack of appropriate information. Topological maps then offer a balance between computational cost and accuracy. One of the most well-known unsupervised learning methods for topological mapping is growing neural gas (GNG). Unfortunately, it is difficult to increase the learning speed due to the traditional iterative method. Consequently, we propose a new method for topological mapping, called simplified multi-scale batch-learning GNG, by applying a mini-batch strategy in the learning process. The proposed method has been implemented on a quadcopter for indoor mapping applications. In addition, the topological maps are also combined with the tracking data of the quadcopter to generate a new global map. The combination is simple yet robust, based on rotation and translation strategies. Thus, the quadcopter is able to run the algorithms in real-time and maintain its performance above 30 fps.