You've already accepted an answer, but I think that part of the answer needs to be made clearer...
A SOM is always topological in nature. It is essentially embedding a 2D manifold in the higher-dimensional space of your data.
At an intuitive level, both k-means and SOM are moving nodes towards denser areas of your space. With k-means, the nodes move freely, with no direct relationship to each other. And a node that is responsible for zero or one data points is degenerate and the k-means algorithm must avoid this situation.
With SOM, when a node moves towards the data, it pulls neighboring nodes in the 2D manifold along with it. This naturally maintains a topology embedded in the data space. And a node can be responsible for 0 or 1 data points with no problem. (Such nodes are sitting in empty space, pulled by their neighbors in all directions. In some sense, they might be an artifact of a manifold, but in another sense they are interpolating between denser space.)
So there isn't some kind of phase change where a SOM goes from not topological to topological. Rather, as the number of SOM nodes increases, you get a higher-resolution manifold.
If you fit a 2x3 (6 node) SOM to the Iris data, you'll get something much more like k-means with 6 nodes than if you fit a 10x15 (150 node) SOM. So I think of it that a low-resolution SOM looks more like the non-topological k-means that is doing a similar task, but a high-resolution SOM's topological nature will be more visible.