Hi, I have recently encountered these two definitions of a sequential space(http://en.wikipedia.org/wiki/Sequential_space) and a space of countable tightness(http://en.wikipedia.org/wiki/Countably_generated_space). . And I seem to have difficulty understanding what is the difference between these two definitions. For example, I know that the space of ultrafilters over ,say, R or N is not weakly Frechet Urysohn so it should not be sequential. But how can one show it directly from the definition? Also, Does these spaces have countble tightness? Thanks!

Hi, I have recently encountered these two definitions of a sequential space (http://en.wikipedia.org/wiki/Sequential_space) and a space of countable tightness (http://en.wikipedia.org/wiki/Countably_generated_space). And I seem to have difficulty understanding what is the difference between these two definitions. For example, I know that the space of ultrafilters over ,say, R or N is not weakly Frechet Urysohn so it should not be sequential. But how can one show it directly from the definition? Also, Does these spaces have countble tightness? Thanks!