Classical-type characterizations of non-metrizable ANE(n)-spaces

Valentin Gutev; Vesko Valov

Fundamenta Mathematicae (1994)

  • Volume: 145, Issue: 3, page 243-259
  • ISSN: 0016-2736

Abstract

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The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is L C n - 1 C n - 1 (resp., L C n - 1 ) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.

How to cite

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Gutev, Valentin, and Valov, Vesko. "Classical-type characterizations of non-metrizable ANE(n)-spaces." Fundamenta Mathematicae 145.3 (1994): 243-259. <http://eudml.org/doc/212045>.

@article{Gutev1994,
abstract = {The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is $LC^\{n-1\} & C^\{n-1\}$ (resp., $LC^\{n-1\}$) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.},
author = {Gutev, Valentin, Valov, Vesko},
journal = {Fundamenta Mathematicae},
keywords = {absolute (neighborhood) extensor in dimension n; n-regular base; n-regular extension operator; Kuratowski-Dugundji theorem; extensors},
language = {eng},
number = {3},
pages = {243-259},
title = {Classical-type characterizations of non-metrizable ANE(n)-spaces},
url = {http://eudml.org/doc/212045},
volume = {145},
year = {1994},
}

TY - JOUR
AU - Gutev, Valentin
AU - Valov, Vesko
TI - Classical-type characterizations of non-metrizable ANE(n)-spaces
JO - Fundamenta Mathematicae
PY - 1994
VL - 145
IS - 3
SP - 243
EP - 259
AB - The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is $LC^{n-1} & C^{n-1}$ (resp., $LC^{n-1}$) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.
LA - eng
KW - absolute (neighborhood) extensor in dimension n; n-regular base; n-regular extension operator; Kuratowski-Dugundji theorem; extensors
UR - http://eudml.org/doc/212045
ER -

References

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  1. [1] A. Chigogidze, Noncompact absolute extensors in dimension n, n-soft mappings, and their applications, Izv. Akad. Nauk SSSR 50 (1) (1986), 156-180 (in Russian); English transl.: Math. USSR-Izv. 28 (1987), 151-174. Zbl0603.54018
  2. [2] A. Dranishnikov, Absolute extensors in dimension n and dimension-raising n-soft maps, Uspekhi Mat. Nauk 39 (5) (1984), 55-95 (in Russian); English transl.: Russian Math. Surveys 39 (1984). Zbl0572.54012
  3. [3] J. Dugundji, Absolute neighborhood retracts and local connectedness in arbitrary metric spaces, Compositio Math. 13 (1958), 229-246. Zbl0089.38903
  4. [4] V. Filippov, On the dimension of products of topological spaces, Fund. Math. 106 (1980), 181-212 (in Russian). Zbl0464.54042
  5. [5] V. Gutev, Selections for quasi-l.s.c. mappings with uniformly equi- L C n range, Set-Valued Anal. 1 (1993), 319-328. Zbl0809.54016
  6. [6] R. Haydon, On a problem of Pełczyński: Milutin spaces, Dugundji spaces and AE(0-dim), Studia Math. 52 (1974), 23-31. Zbl0294.46016
  7. [7] K. Kuratowski, Sur les espaces localement connexes et péaniens en dimension n, Fund. Math. 24 (1935), 269-287. Zbl0011.04002
  8. [8] E. Michael, Continuous selections II, Ann. of Math. 64 (1956), 562-580. Zbl0073.17702
  9. [9] R. Pol and E. Puzio-Pol, Remarks on Cartesian products, Fund. Math. 93 (1976), 57-69. 
  10. [10] E. V. Ščepin [E. V. Shchepin], Functors and uncountable powers of compacta, Uspekhi Mat. Nauk 36 (3) (1981), 3-62 (in Russian); English transl.: Russian Math. Surveys 36 (1981). Zbl0463.54009
  11. [11] L. Shirokov, On AE(n)-compacta and n-soft mappings, Sibirsk. Mat. Zh. 33 (1992), 151-156 (in Russian). Zbl0873.54020
  12. [12] H. Toruńczyk, Concerning locally homotopy negligible sets and characterizations of l 2 -manifolds, Fund. Math. 101 (1978), 93-110. Zbl0406.55003
  13. [13] V. Valov, Another characterization of AE(0)-spaces, Pacific J. Math. 127 (1987), 199-208. Zbl0593.54033

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