In e-learning settings, technology plays several crucial roles in the teaching. In addition to enabling students to gain remote access to teaching, it can also change the way time, space and presence are perceived by students and teachers. This paper attempts to analyse and discuss the consequences of the transparency or visibility of e-learning technology inside and outside the classroom and highlight its opportunities of multiplying the learning spaces. In order to be able to differentiate between learning that occurs in the same place and learning that occurs in more places at the same time across virtual and physical spaces, the paper therefore introduces the concepts of "idiotopic" and "polytopic" learning settings. Furthermore, it argues that the development of "polytopic" learning designs could help address a potential e-learning demand for teaching presences in more places at the same time.