Open AccessStrengthening connected Tychonoff topologies
Author(s) -
Dmitri Shakhmatov,
Mikhail Tkachenko,
Vladimir V. Tkachuk,
Richard G. Wilson
Publication year - 2002
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 13
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2002.2058
Subject(s) - tychonoff space , mathematics , topological group , topology (electrical circuits) , space (punctuation) , topological space , discrete mathematics , combinatorics , discrete group , pure mathematics , group (periodic table) , computer science , physics , operating system , quantum mechanics
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