We continue the study of g-convergence given in 2005 [Caldas, M.; Jafari, S. On g-US spaces. Stud. Cercet. Ştiinţ. Ser. Mat. Univ. Bacău 14 (2004), 13–19 (2005).] by introducing the sequential g-closure operator and we prove that the product of g-sequential spaces is not g-sequential by giving an example. We further investigate sequential g-continuity in topological spaces and present interesting theorems which are also new for the real case. It is shown that in a topological space the property of being g-sequential implies sequential, g-Fréchet implies Fréchet and g-Fréchet implies g-sequential. However, the inverse conclusions are not true and some counter examples are given. Also, we show that strongly g-continuous image of a g-sequential space is g-sequential, if the map is quotient. Finally, we obtain a necessary and sufficient condition for a topological space to be g-sequential in terms of a sequentially g-quotient map.


Additional Information


Renukadevi, V., Vijayashanthi, P.