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A topology generated by eventually different functions. (English) Zbl 0883.03033
The topology $$\mathcal E$$ on $$\omega^\omega$$ mentioned in the title is generated by the sets $$U_{s,F}=\{x\in\omega^\omega: s\subseteq x\mathrel{\&} (\forall f\in F)(\forall i\geq n)\;f(i)\neq x(i)\}$$ for $$s\in2^n$$, $$n\in\omega$$, and finite sets $$F\subseteq\omega^\omega$$. The space $$(\omega^\omega,{\mathcal E})$$ is a Tikhonov c.c.c. space in which no open set is meager. Cardinal coefficients for the ideal of meager sets $${\mathcal I}_{\mathcal E}$$ are estimated by cardinals of Cichoń’s diagram and some applications of Martin’s axiom and anti-Martin’s axiom are obtained. It is proved that the additivity of $${\mathcal I}_{\mathcal E}$$ is $$\omega_1$$ and the minimal size of a base of $${\mathcal I}_{\mathcal E}$$ is $$\mathfrak c$$.

##### MSC:
 03E15 Descriptive set theory 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) 03E40 Other aspects of forcing and Boolean-valued models 03E50 Continuum hypothesis and Martin’s axiom 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
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