Every topological space is semi-pre-$_{\alpha} T_{1/2}$.
 作者： Toshihiro Ohba,  Jun-iti Umehara 刊名： Mem. Fac. Sci., Kochi Univ., Ser. A 21, 89-92 (2000)., 2000, pp.89-92 来源数据库： ZBMATH期刊 原始语种摘要： Introduction: In [Rend. Circ. Mat. Palermo, II. Ser. 19, 89-96 (1970; Zbl 0231.54001)] {\it N. Levine} defined and studied generalized closed sets (briefly $g$-closed sets) and $T_{1/2}$ spaces. Since then many modified notions and theorems in this direction were introduced and investigated. In [Mem. Fac. Sci., Kochi Univ., Ser. A 16, 35-48 (1995; Zbl 0833.54001)] {\it J. Dontchev} defined and studied generalized semi-pre-closed sets (briefly gsp-closed sets) and semi-pre-$T_{1/2}$ spaces. In [ibid. 20, 33-46 (1999; Zbl 0921.54001)] {\it M. K. R. S. Veera Kumar} defined semi-pre-generalized closed sets (briefly spg-closed sets) and semi-pre-$T_{1/4}$ spaces. In his thesis [Fac. Sci. Kochi Univ., February 1999] the first author remarked that every topological space is a semi-pre-$T_{1/4}$... space. \par In this note the authors define $\alpha$-semi-pre-generalized closed sets (briefly $\alpha$spg-closed sets) and semi-pre-$_\alpha T_{1/2}$ spaces and show that every topological space is a semi-pre-$_\alpha T_{1/2}$ space; consequently every topological space is a semi-pre-$T_{1/4}$ space.

• alpha　接字母顺序的
• topological　拓扑的
• generalized　广义
• closed　闭路的
• briefly　简洁的
• space　宇宙
• thesis　命题
• defined　定义
• studied　学习
• direction　方向