RNA representation is one of the most important issues in bioinformatics. A challenge, however, is achieving a correct representation that is able to encode the directionality, secondary and primary structure. One possible solution is the RNA graph representation and its associate tree; however, it fails to encode the directionality of the RNA molecule. Therefore, a succession based on the tree representation is proposed as an alternative. From this novel succession, we have defined three metrics in order to compare the similarity between RNAs. Finally, we have used the properties of pretopological spaces which were generated from the metrics as a cluster tool. This methodology has allowed the classification of an RNA hairpin, which was mutated in two different positions.