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We develop a calculus for the oscillation index of Baire one functions using gauges analogous to the modulus of continuity.
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 is a -space, then . Moreover, we will show relative versions of three well-known cardinal inequalities.
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