Shakhmatov, D.; Tkachenko, M.; Tkachuk, VV.; Wilson, RG. (2002). Strengthening connected Tychonoff topologies. Applied General Topology. 3(2):113-131. https://doi.org/10.4995/agt.2002.2058
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/82060
Title:
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Strengthening connected Tychonoff topologies
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Author:
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Shakhmatov, Dimitri
Tkachenko, Mikhail
Tkachuk, Vladimir V.
Wilson, Richard G.
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Issued date:
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Abstract:
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[EN] 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 ...[+]
[EN] 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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Subjects:
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Connected
,
Strongly σ-discrete
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Submetrizable
,
Regular open set
,
Dense subset
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Topological group
,
Quotient group
,
Free topological group
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Copyrigths:
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Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
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Source:
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Applied General Topology. (issn:
1576-9402
) (eissn:
1989-4147
)
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DOI:
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10.4995/agt.2002.2058
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Publisher:
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Universitat Politècnica de València
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Publisher version:
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https://doi.org/10.4995/agt.2002.2058
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Project ID:
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info:eu-repo/grantAgreement/CONACyT//400200-5-28411E/
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Thanks:
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The research was supported by Mexican National Council fo Science and Technology (CONACYT), grant number 400200-5-28411E
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Type:
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Artículo
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