Nowhere dense choices and π-weight

Istvan Juhász; William A. R. Weiss

Published: 1986-09-30

Vol. 2 (1986)

Nowhere dense choices and π-weight

Istvan Juhász , William A. R. Weiss

Abstract

The paper is devoted to inequalities between π₀(X) and π_d(X) where
π₀(X) := min{π(U): U open and non-empty subset of X},
π_d(X) := min{|B|: every open and dense subset of X containes an element from B}.
From these definitions π_d(X) ≤ π₀(X) for every space X. In the paper we construct a space X for which π_d(X)=ω₁ and π₀(X)=2^ℵ₀.

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Juhász, I., & Weiss, W. A. R. (1986). Nowhere dense choices and π-weight. Annales Mathematicae Silesianae, 2, 85–91. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14327

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