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A note on extension theory and direct limits


Mardešić, Sibe; Rubin, Lenny R.
A note on extension theory and direct limits // Publicationes mathematicae Debrecen, 75 (2009), 437-445 (međunarodna recenzija, članak, znanstveni)


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Naslov
A note on extension theory and direct limits

Autori
Mardešić, Sibe ; Rubin, Lenny R.

Izvornik
Publicationes mathematicae Debrecen (0033-3883) 75 (2009); 437-445

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
absolute extensor; extension dimension; cohomological dimension; CW-complex; direct system; direct limit; colimit; normal space; compact Hausdorff space; locally compact space; compactly generated space; k-space; Tychonoff plank; weak topology.

Sažetak
The direct limit of a direct sequence consisting of normal spaces and closed inclusion mappings is a normal space. This result does not generalize to direct systems because there exist direct systems of compact Hausdorff spaces and closed inclusion mappings whose limit spaces fail to be normal. Introducing additional assumptions, K. Morita obtained normality of the limit space also for systems of normal spaces. Replacing normality of the spaces in the system by the property that a given K (in particular, a CW-complex K) is an absolute extensor for these spaces, the analogue of Morita's theorem remains valid, i.e., K is an absolute extensor for the limit space. This holds even under a weaker version of Morita's additional assumptions. In the case of direct sequences, these weaker conditions are always satisfied and therefore, the improved Morita theorem implies the result for direct sequences of normal spaces.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
037-0372791-2802 - Teorija dimenzije i oblika (Sibe Mardešić, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Profili:

Avatar Url Sibe Mardešić (autor)

Citiraj ovu publikaciju

Mardešić, Sibe; Rubin, Lenny R.
A note on extension theory and direct limits // Publicationes mathematicae Debrecen, 75 (2009), 437-445 (međunarodna recenzija, članak, znanstveni)
Mardešić, S. & Rubin, L. (2009) A note on extension theory and direct limits. Publicationes mathematicae Debrecen, 75, 437-445.
@article{article, year = {2009}, pages = {437-445}, keywords = {absolute extensor, extension dimension, cohomological dimension, CW-complex, direct system, direct limit, colimit, normal space, compact Hausdorff space, locally compact space, compactly generated space, k-space, Tychonoff plank, weak topology.}, journal = {Publicationes mathematicae Debrecen}, volume = {75}, issn = {0033-3883}, title = {A note on extension theory and direct limits}, keyword = {absolute extensor, extension dimension, cohomological dimension, CW-complex, direct system, direct limit, colimit, normal space, compact Hausdorff space, locally compact space, compactly generated space, k-space, Tychonoff plank, weak topology.} }

Časopis indeksira:


  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus