It is Deleuze & Guattari's description of smooth and striated cultural spaces (Deleuze & Guattari, 1988) which informs this exploration of pedagogical alternatives within the learning environments of cyberspace. Digital spaces work to constitute subject and text in ways which are distinct, and it is awareness of this distinctiveness which must inform our engagement with the internet as a space for learning and teaching. By using Deleuze & Guattari's conceptualisation of the smooth and the striated, the author works towards a way of understanding how a theorisation of internet "topography" can inform pedagogical choice within online learning contexts. The author begins with a summary of the relation between the striated and the smooth as defined by Deleuze & Guattari, and moves on to consider how this distinction can be extended into the environments of cyberspace. She then explores how a pedagogical approach might be developed which attempts to inhabit "smooth" internet spaces, and ends with a consideration of the virtual learning environment or "e-learning system" which, in defining itself as a space of containment, regulation and efficient progression, functions as a strongly striating element within pedagogical web space.