Baire functions and spaces of Baire functions

The paper considers (1) the tightness of spaces of Baire functions and their subspaces endowed with the topology of pointwise convergence; (2) $Z_{\sigma}$-mappings of $K$-analytic spaces; (3) $K_{\sigma}$-analytic spaces (Tychonoff spaces which are $Z_{\sigma}$-images of $K$-analytic spaces).