Strengthening connected Tychonoff topologies
DOI:
https://doi.org/10.4995/agt.2002.2058Keywords:
Connected, Strongly σ-discrete, Submetrizable, Regular open set, Dense subset, Topological group, Quotient group, Free topological groupAbstract
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) ≤ N0 admits a finer strongly σ-discrete connected Tychonoff topology of weight 2c. 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.
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