Strengthening connected Tychonoff topologies | Zendy

Dimitri Shakhmatov | Zendy; Mikhail Tkachenko | Zendy; Vladimir V. Tkachuk | Zendy; Richard G. Wilson | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Strengthening connected Tychonoff topologies

Author(s) -

Dimitri 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

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research