TY - JOUR
AU - MÃ¡rquez, Edgar
PY - 2023/10/02
Y2 - 2024/10/04
TI - Countable networks on Malykhin's maximal topological group
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 24
IS - 2
SE -
DO - 10.4995/agt.2023.18517
UR - https://polipapers.upv.es/index.php/AGT/article/view/18517
SP - 239-246
AB - <p>We present a solution to the following problem: Does every countable and non-discrete topological (Abelian) group have a countable network with infinite elements? In fact, we show that no maximal topological space allows for a countable network with infinite elements. As a result, we answer the question in the negative. The article also focuses on Malykhin's maximal topological group constructed in 1975 and establishes some unusual properties of countable networks on this special group G. We show, in particular, that for every countable network N for G, the family of finite elements of N is also a network for G.</p>
ER -