Quotients of Strongly Realcompact Groups

• Autorzy: L. Morales , M. Tkachenko
• Języki publikacji: EN

Abstrakty

EN

A topological group is strongly realcompact if it is topologically isomorphic to a closed subgroup of a product of separable metrizable groups. We show that if H is an invariant Čech-complete subgroup of an ω-narrow topological group G, then G is strongly realcompact if and only if G/H is strongly realcompact. Our proof of this result is based on a thorough study of the interaction between the P-modification of topological groups and the operation of taking quotient groups.

Słowa kluczowe

EN

Extension of groups; Strongly realcompact; Strongly Dieudonné complete; P-modification; Pgroup; Quotient group

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2016
• Tom: 4
• Numer: 1
• Strony: 9-17

Daty

otrzymano

2015-04-18

zaakceptowano

2016-06-17

online

2016-08-01

Twórcy

autor

L. Morales

• Keiser University Latin American Campus, De la gasolinera UNO dos cuadras al sur, San Marcos, Carazo, Nicaragua

autor

M. Tkachenko

• Universidad Autónoma Metropolitana, Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, C.P. 09340, Mexico D.F., Mexico

Bibliografia

• [1] A.V. Arhangel’skii, M. G. Tkachenko, Topological groups and related structures, Atlantis Studies in Mathematics, I. Atlantis Press, Paris–Amsterdam; World Scientific Publishing Co. Pte. Ltd., Hackensack, New Jork (2008). xiv+781 pp. ISBN: 978-90- 78677-06-2.
• [2] R. Engelking, General Topology, Heldlermann Verlag, Berlin (1989).
• [3] D. L. Grant, Topological groups which satisfy an open mapping theorem, Pacific J. Math. 68 (1977), 411–423.
• [4] C. Hernandez, M.G. Tkachenko, A note on !-modification and completeness concepts, Bol. Soc.Mat. Mexicana (3) 8 (2002), 93–96.
• [5] G. Lukász, Compact-like topological groups, Research and Exposition in Mathematics, 31. Heldermann Verlag, Lemgo, 2009.
• [6] V. G. Pestov, Embeddings and condensations of topological groups, Math. Notes 31, 3–4, 228–230. Russian original in: Mat. Zametki 31 (1982), 442–446. [Crossref]
• [7] W. Roelcke, S. Dierolf, Uniform Structures on Topological Groups and Their Quotients, McGraw-Hill (1981).
• [8] M. G. Tkachenko, C. Hernández-García, and M.A. López Ramírez, Strong realcompactness and strong Dieudonné completeness in topological groups, Topol. Appl. 159 (2012), 1948–1955. [WoS]
• [9] M. Ursul, Embeddings of locally precompact groups in locally pseudocompact ones, Izv. Akad. Nauk Moldav. SSR Ser. Fiz.-Tekh. Mat. Nauk 3 (1989), 54–56 (in Russian).

Identyfikatory

DOI

10.1515/taa-2016-0002