Uniform topology onEQ-algebras

Jiang Yang, Xiao Long Xin, and Peng Fei He. "Uniform topology onEQ-algebras." Open Mathematics 15.1 (2017): 354-364. <http://eudml.org/doc/288035>.

@article{JiangYang2017,
abstract = {In this paper, we use filters of an EQ-algebra E to induce a uniform structure (E, 𝓚), and then the part 𝓚 induce a uniform topology 𝒯 in E. We prove that the pair (E, 𝒯) is a topological EQ-algebra, and some properties of (E, 𝒯) are investigated. In particular, we show that (E, 𝒯) is a first-countable, zero-dimensional, disconnected and completely regular space. Finally, by using convergence of nets, the convergence of topological EQ-algebras is obtained.},
author = {Jiang Yang, Xiao Long Xin, Peng Fei He},
journal = {Open Mathematics},
keywords = {Uniform space; Topological EQ-algebra; Filter; Converge sequence; uniform space; topological $EQ$-algebra; filter; converge sequence},
language = {eng},
number = {1},
pages = {354-364},
title = {Uniform topology onEQ-algebras},
url = {http://eudml.org/doc/288035},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Jiang Yang
AU - Xiao Long Xin
AU - Peng Fei He
TI - Uniform topology onEQ-algebras
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 354
EP - 364
AB - In this paper, we use filters of an EQ-algebra E to induce a uniform structure (E, 𝓚), and then the part 𝓚 induce a uniform topology 𝒯 in E. We prove that the pair (E, 𝒯) is a topological EQ-algebra, and some properties of (E, 𝒯) are investigated. In particular, we show that (E, 𝒯) is a first-countable, zero-dimensional, disconnected and completely regular space. Finally, by using convergence of nets, the convergence of topological EQ-algebras is obtained.
LA - eng
KW - Uniform space; Topological EQ-algebra; Filter; Converge sequence; uniform space; topological $EQ$-algebra; filter; converge sequence
UR - http://eudml.org/doc/288035
ER -