# A dimension raising hereditary shape equivalence

Fundamenta Mathematicae (1996)

- Volume: 149, Issue: 3, page 265-274
- ISSN: 0016-2736

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topDijkstra, Jan. "A dimension raising hereditary shape equivalence." Fundamenta Mathematicae 149.3 (1996): 265-274. <http://eudml.org/doc/212123>.

@article{Dijkstra1996,

abstract = {We construct a hereditary shape equivalence that raises transfinite inductive dimension from ω to ω+1. This shows that ind and Ind do not admit a geometric characterisation in the spirit of Alexandroff's Essential Mapping Theorem, answering a question asked by R. Pol.},

author = {Dijkstra, Jan},

journal = {Fundamenta Mathematicae},

keywords = {hereditary shape equivalence; transfinite inductive dimension},

language = {eng},

number = {3},

pages = {265-274},

title = {A dimension raising hereditary shape equivalence},

url = {http://eudml.org/doc/212123},

volume = {149},

year = {1996},

}

TY - JOUR

AU - Dijkstra, Jan

TI - A dimension raising hereditary shape equivalence

JO - Fundamenta Mathematicae

PY - 1996

VL - 149

IS - 3

SP - 265

EP - 274

AB - We construct a hereditary shape equivalence that raises transfinite inductive dimension from ω to ω+1. This shows that ind and Ind do not admit a geometric characterisation in the spirit of Alexandroff's Essential Mapping Theorem, answering a question asked by R. Pol.

LA - eng

KW - hereditary shape equivalence; transfinite inductive dimension

UR - http://eudml.org/doc/212123

ER -

## References

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- [7] J. J. Dijkstra and J. Mogilski, A geometric approach to the dimension theory of infinite-dimensional spaces, in: Proc. 8th Ann. Workshop Geom. Topology, Univ. of Wisconsin-Milwaukee, 1991, 59-63.
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- [14] W. Hurewicz, Ueber unendlich-dimensionale Punktmengen, Proc. Akad. Amsterdam 31 (1928), 916-922. Zbl54.0620.05
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- [16] J. van Mill and J. Mogilski, Property C and fine homotopy equivalences, Proc. Amer. Math. Soc. 90 (1984), 118-120. Zbl0548.57006
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