Almost continuity vs closure continuity. (English) Zbl 1090.54503

Saleemi, B. A.; Shahzad, N.; Alghamdi, M. A.

Arch. Math., Brno 37, No. 1, 39-44 (2001).

The authors study relationships between various notions of generalized continuity for mappings between (non necessarily Hausdorff) topological spaces. They prove that a mapping is “closure continuous” provided it is simultaneously “weakly continuous” and “almost continuous in the sense of T. Husain”.
The question on strengthening the result asked by the authors on p.42 has trivially positive answer. The proof is almost the same as that of the main result.

Reviewer: Ondřej Kalenda (Praha)

MSC:

54C08

Weak and generalized continuity

Keywords:

almost continuous function; closure continuous function; weakly continuous function