Strict Topological Extensions and Power-objects for b-convergence

We consider antiform b-convergence as a common generalization of preuniform convergence, well-known point-convergences and suitable set-convergences as well. The corresponding defined category ab-CONV is a topological construct which is cartesian closed. Then the above mentioned categories can be nicely embedded into ab-CONV. Moreover, we will establish a one-to-one correspondence between some b-convergence and the related symmetric strict topological extension.