# Counting connected components of the complement of the image of a codimension 1 map

Compositio Mathematica (1994)

- Volume: 93, Issue: 1, page 37-47
- ISSN: 0010-437X

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topNuño Ballesteros, Juan J.. "Counting connected components of the complement of the image of a codimension 1 map." Compositio Mathematica 93.1 (1994): 37-47. <http://eudml.org/doc/90313>.

@article{NuñoBallesteros1994,

author = {Nuño Ballesteros, Juan J.},

journal = {Compositio Mathematica},

keywords = {singular set; number of components of the complement; proper continuous map between connected manifolds; Alexander-Čech cohomology},

language = {eng},

number = {1},

pages = {37-47},

publisher = {Kluwer Academic Publishers},

title = {Counting connected components of the complement of the image of a codimension 1 map},

url = {http://eudml.org/doc/90313},

volume = {93},

year = {1994},

}

TY - JOUR

AU - Nuño Ballesteros, Juan J.

TI - Counting connected components of the complement of the image of a codimension 1 map

JO - Compositio Mathematica

PY - 1994

PB - Kluwer Academic Publishers

VL - 93

IS - 1

SP - 37

EP - 47

LA - eng

KW - singular set; number of components of the complement; proper continuous map between connected manifolds; Alexander-Čech cohomology

UR - http://eudml.org/doc/90313

ER -

## References

top- 1 Biasi, C., Motta, W. and Saeki, O.: A note on separation properties of codimension-1 immersions with normal crossings, Topology and its applications (to appear). Zbl0791.57020MR1237182
- 2 Biasi, C., Motta, W. and Saeki, O.: A remark on the separation by immersions in codimension-1, preprint (1992). Zbl0829.57017MR1314617
- 3 Biasi, C. and Romero Fuster, M.C.: A converse of the Jordan-Brouwer theorem, Illinois J. Math.36 (1992) 500-504. Zbl0739.57020MR1161979
- 4 Feighn, M.E.: Separation properties of codimension-1 immersions, Topology27 (1988) 319-321. Zbl0658.57019MR963634
- 5 Golubitsky, M. and Guillemin, V.: Stable Mappings and Their Singularities. Grad Text in Math.14, Springer-Verlag, Berlin, Heidelberg and New York, 1973. Zbl0294.58004MR341518
- 6 Izumiya, S. and Marar, W.L.: The Euler number of a topologically stable singular surface in a 3-manifold, preprint (1992). MR1250214
- 7 Nuño Ballesteros, J.J. and Romero Fuster, M.C.: Separation properties of continuous maps in codimension 1 and geometrical applications. Topology and its Applications46 (1992) 107-111. Zbl0787.57012MR1184109
- 8 Saeki, O.: A separation property of codimension-1 maps with a normal crossing point, preprint (1992).
- 9 Spanier, E.H.: Algebraic Topology. Tata McGraw-Hill Publ. Co. Ltda., Bombay-New Delhi, 1966. Zbl0145.43303MR210112
- 10 Vaccaro, M.: Proprietà topologiche delle rappresentazioni localmente biunivoche. Math. Ann.133 (1957) 173-184. Zbl0084.39302MR87108

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