Topology and its Applications 154 (2007) 1307–1313 www.elsevier.com/locate/topol Some new topological cardinal inequalities Fidel Casarrubias-Segura a , Agustín Contreras-Carreto b,∗ , Alejandro Ramírez-Páramo b a Departamento de Matemáticas Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, México, DF 04510, Mexico b Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y Río Verde, Colonia San Manuel, Ciudad Universitaria, Puebla, Pue., 72570 Mexico Received 17 June 2005; received in revised form 9 September 2005; accepted 9 September 2005 Abstract In this paper we make use of the Pol–Šapirovski˘ ı’s technique to prove several cardinal inequalities, which generalize other well-known inequalities.  2006 Elsevier B.V. All rights reserved. MSC: 54A25 Keywords: Cardinal functions; Cardinal inequalities 1. Introduction Among the best known theorems concerning cardinal functions are those which give an upper bound on the car- dinality of a space in terms of other cardinal invariants. In [5], Hodel classified the bounds on |X| in two categories namely easy and difficult to prove. For instance, the following inequalities are in the difficult category: (1) (Arhangel’skiˇ ı) If X is a T 2 -space then |X|  2 L(X)ψ(X)t(X) . (2) (Hajnal–Juhász) If X is a T 2 -space then |X|  2 c(X)χ(X) . (3) (Charlesworth) If X is a T 1 -space, |X|  psw(X) L(X)ψ(X) . (4) (Bell–Ginsburg–Woods) If X ∈ T 4 , |X|  2 wL(X)χ(X) . In [4] Fedeli introduces three cardinal functions, two of these are lc and aql, and he uses the language of elementary submodels to prove: (5) If X is a T 2 -space, |X|  2 aql(X)ψ c (X)t(X) . (6) If X is a T 2 -space, |X|  2 lc(X)πχ(X)ψ c (X) . These inequalities improve (1) and (2), respectively. Other generalizations of (1) and (2) have also been proved by Shu-Hao [10]: (7) If X is a T 2 -space, |X|  2 ql(X)ψ c (X)t(X) . * Corresponding author. E-mail addresses: guli@servidor.unam.mx (F. Casarrubias-Segura), acontri@fcfm.buap.mx (A. Contreras-Carreto), aparamo@fcfm.buap.mx (A. Ramírez-Páramo). 0166-8641/$ – see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.topol.2005.09.014