E_1

Last-modified: 2012-11-05 (月) 21:12:01

Definition

  • A topological space (X, τ) is called an E_1 space if for x ∈ X imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cdisplaystyle%7b%5crm%20Cl%7d%28%5c%7bx%5c%7d%29=%5ccap_%7bn=0%7d%5e%5cinfty%20C_n%5e%7b%28x%29%7d%20%5c%5d%7d%25.png , where C_n^(x) is a closed neighborhood of x.

Reference

  • Aull, C. E., "Some base axioms for topology involving enumerability.", 1971 General Topology and its Relations to Modern Analysis and Algebra, III (Proc. Conf., Kanpur, 1968) pp. 55-61.