Using the idea of ic-open sets, we introduce and investigate topological qualities an ic-closure, ic-interior, ic-limit points, ic-derived, ic-border, ic-frontier, ic-exterior a set. Introduce concepts "ic-continuous mappings," "ic-open "ic-irresolute "ic-totally continuous "ic-homeomorphism," then look into some properties these mappings

Abstract For any open hyperbolic Riemann surface $X$, the Bergman kernel $K$, logarithmic capacity $c_{\beta }$, and analytic $c_{B}$ satisfy inequality chain $\pi K \geq c^2_{\beta } c^2_B$. Moreover, equality holds at a single point between two of three quantities if only $X$ is biholomorphic to disk possibly less relatively closed polar set. We extend by showing that $c_{B}^2 \pi v^{-1}(X)$ ...

The aim of this paper is to investigate some properties of pre-I-open sets, semi-I-open sets and b-I-open sets in ideal topological spaces. Some relationships of pre-I-open sets, semi-I-open sets and b-I-open sets in ideal topological spaces are discussed. Moreover, decompositions of continuity are provided. 2000 Mathematics Subject Classification: 54A05, 54A10, 54C08, 54C10.