Kohonen's self-organizing maps are a recognized tool for finding representative data vectors and clustering the data. To what extent is it possible to preserve the topology of the data in the constructed planar map? We address the question looking at distal data points located at the peripherals of the data cloud and their position in the provided map. Several data sets have been investigated; we present the results for two of them: the Glass data (dimension d=7) and the Ionosphere data (dimension d=32). It was found that the distal points are reproduced either at the edges (borders) of the map, or at the peripherals of dark regions visualized in the maps.