@article{Shakhmatov_Tkachenko_Tkachuk_Wilson_2002, title={Strengthening connected Tychonoff topologies}, volume={3}, url={https://polipapers.upv.es/index.php/AGT/article/view/2058}, DOI={10.4995/agt.2002.2058}, abstractNote={<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>}, number={2}, journal={Applied General Topology}, author={Shakhmatov, Dimitri and Tkachenko, Mikhail and Tkachuk, Vladimir V. and Wilson, Richard G.}, year={2002}, month={Oct.}, pages={113–131} }