On preservation of normality

The theory of normal spaces is treated in this paper. In section 1 we define a new type of mappings called paranormal, and we prove that a continuous mapping onto a normal space is paranormal if and only if its domain is normal. The section ends with the study of relativized notions of normality and paracompactness. In section 2 we study the normalitv of the products. Finally, section 3 contains the discussion of counterexamples relevant to the definition and theorems in the previous sections.