Characteristics of ${\alpha g}_{(\gamma,\delta )}$-Irresolute Maps

The intention of this paper is to bring forth new maps namely ${\alpha g}_{(\gamma,\delta )}$- irresolute and ${\alpha g}_{(\gamma,\delta )}$-homeomorphism using ${\alpha g}_{\gamma }$-open sets and study their properties. This new concept enables us to determine the conditions under which maps and inverse maps, preserve ${\alpha g}_{\gamma }$-open sets. We derive the relation between ${\alpha g}_{(\gamma,\delta )}$- irresolute, $\alpha g$-$(\gamma,\delta)$-open, $\alpha g$-$(\gamma,\delta)$-closed maps and ${\alpha g}_{(\gamma,\delta )}$-homeomorp-hism in topological spaces.