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https://doi.org/10.3336/gm.51.2.11

Certain weakly generated noncompact pseudo-compact topologies on Tychonoff cubes

Leonard R. Rubin   ORCID icon orcid.org/0000-0002-1108-0267 ; Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019, USA

Puni tekst: engleski, pdf (101 KB) str. 447-452 preuzimanja: 237* citiraj
APA 6th Edition
Rubin, L.R. (2016). Certain weakly generated noncompact pseudo-compact topologies on Tychonoff cubes. Glasnik matematički, 51 (2), 447-452. https://doi.org/10.3336/gm.51.2.11
MLA 8th Edition
Rubin, Leonard R.. "Certain weakly generated noncompact pseudo-compact topologies on Tychonoff cubes." Glasnik matematički, vol. 51, br. 2, 2016, str. 447-452. https://doi.org/10.3336/gm.51.2.11. Citirano 20.10.2021.
Chicago 17th Edition
Rubin, Leonard R.. "Certain weakly generated noncompact pseudo-compact topologies on Tychonoff cubes." Glasnik matematički 51, br. 2 (2016): 447-452. https://doi.org/10.3336/gm.51.2.11
Harvard
Rubin, L.R. (2016). 'Certain weakly generated noncompact pseudo-compact topologies on Tychonoff cubes', Glasnik matematički, 51(2), str. 447-452. https://doi.org/10.3336/gm.51.2.11
Vancouver
Rubin LR. Certain weakly generated noncompact pseudo-compact topologies on Tychonoff cubes. Glasnik matematički [Internet]. 2016 [pristupljeno 20.10.2021.];51(2):447-452. https://doi.org/10.3336/gm.51.2.11
IEEE
L.R. Rubin, "Certain weakly generated noncompact pseudo-compact topologies on Tychonoff cubes", Glasnik matematički, vol.51, br. 2, str. 447-452, 2016. [Online]. https://doi.org/10.3336/gm.51.2.11

Sažetak
Given an uncountable cardinal ℵ, the product space Iℵ, I=[0,1], is called a Tychonoff cube. A collection of closed subsets of a subspace Y of a Tychonoff cube Iℵ that covers Y determines a weak topology for Y. The collection of compact subsets of Iℵ that have a countable dense subset covers Iℵ. It is known from work of the author and I. Ivanšić that the weak topology generated by this collection is pseudo-compact. We are going to show that it is not compact. The author and I. Ivanšić have also considered weak topologies on some other ``naturally occurring'' subspaces of such Iℵ. The new information herein along with the previous examples will lead to the existence of vast naturally occurring classes of pseudo-compacta any set of which has a pseudo-compact product. Some of the classes consist of Tychonoff spaces, so the product spaces from subsets of these are also Tychonoff spaces.

Ključne riječi
First uncountable ordinal space; products; pseudo-compact; Tychonoff cube; weak topology

Hrčak ID: 170047

URI
https://hrcak.srce.hr/170047

Posjeta: 412 *