## Alejandro Ram\'{\i }rez-P\'aramo, No\'e Trinidad Tapia-Bonilla

*A generalization of a generic theorem in the theory of cardinal invariants of topological spaces *

Comment.Math.Univ.Carolin. 48,1 (2007) 177-187. **Abstract:**The main goal of this paper is to establish a technical result, which provides an algorithm to prove several cardinal inequalities and relative versions of cardinal inequalities related to the well-known Arhangel'skii's inequality: If $X$ is a $T_2$-space, then $|X|\leq 2^{L(X)\chi (X)}$. Moreover, we will show relative versions of three well-known cardinal inequalities.

**Keywords:** cardinal functions, cardinal inequalities

**AMS Subject Classification:** Primary 54A25

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