TY - JOUR
AU - Shakhmatov, Dimitri
AU - Tkachenko, Mikhail
AU - Tkachuk, Vladimir V.
AU - Wilson, Richard G.
PY - 2002/10/01
Y2 - 2024/06/21
TI - Strengthening connected Tychonoff topologies
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 3
IS - 2
SE -
DO - 10.4995/agt.2002.2058
UR - https://polipapers.upv.es/index.php/AGT/article/view/2058
SP - 113-131
AB - <p>The problem of whether a given connected Tychonoff space admits a strictly finer connected Tychonoff topology is considered. We show that every Tychonoff space X satisfying ω (X) ≤ c and c (X) ≤ N<sub>0</sub> admits a finer strongly σ-discrete connected Tychonoff topology of weight 2<sup>c</sup>. We also prove that every connected Tychonoff space is an open continuous image of a connected strongly σ-discrete submetrizable Tychonoff space. The latter result is applied to represent every connected topological group as a quotient of a connected strongly σ-discrete submetrizable topological group.</p>
ER -