Recent years have witnessed a remarkable growth in the way mathematics, informatics, and computer science can process data. In disciplines such as machine learning, pattern recognition, computer vision, computational neurology, molecular biology, information retrieval, etc., many new methods have been developed to cope with the ever increasing amount and complexity of the data. These new methods offer interesting possibilities for processing, classifying and interpreting eye-tracking data. The present paper exemplifies the application of topological arguments to improve the evaluation of eye-tracking data. The task of classifying raw eye-tracking data into saccades and fixations, with a single, simple as well as intuitive argument, described as coherence of spacetime, is discussed, and the hierarchical ordering of the fixations into dwells is shown. The method, namely identification by topological characteristics (ITop), is parameter-free and needs no pre-processing and post-processing of the raw data. The general and robust topological argument is easy to expand into complex settings of higher visual tasks, making it possible to identify visual strategies.