Geodesic
Embedding compacta in Euclidean space of dimension $5$, $4$ and $3$
Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 563-569 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper results concerning the notion of dimension of an embedding, earlier obtained for embeddings of compacta in Euclidean space $E_n$ for $n\geqslant6$, are extended to the case $n=5$. For $n=4$ a reduction of the main problem to the so-called open four-dimensional Poincaré conjecture is given, and some sufficient conditions are given for $n=3$. Bibliography: 14 titles. 
@article{SM_1976_28_4_a8,
     author = {M. A. Shtan'ko},
     title = {Embedding compacta in {Euclidean} space of dimension~$5$, $4$ and~$3$},
     journal = {Sbornik. Mathematics},
     pages = {563--569},
     year = {1976},
     volume = {28},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_28_4_a8/}
}
TY  - JOUR
AU  - M. A. Shtan'ko
TI  - Embedding compacta in Euclidean space of dimension $5$, $4$ and $3$
JO  - Sbornik. Mathematics
PY  - 1976
SP  - 563
EP  - 569
VL  - 28
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1976_28_4_a8/
LA  - en
ID  - SM_1976_28_4_a8
ER  - 
%0 Journal Article
%A M. A. Shtan'ko
%T Embedding compacta in Euclidean space of dimension $5$, $4$ and $3$
%J Sbornik. Mathematics
%D 1976
%P 563-569
%V 28
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1976_28_4_a8/
%G en
%F SM_1976_28_4_a8
M. A. Shtan'ko. Embedding compacta in Euclidean space of dimension $5$, $4$ and $3$. Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 563-569. http://geodesic.mathdoc.fr/item/SM_1976_28_4_a8/

[1] E. E. Moise, “Piecewise linear approximation of homeomorphisms”, Ann. Math., 55 (1952), 215–222 | DOI | MR | Zbl

[2] H. Bothe, “Ein eindimensionals Kompactum in $E^3$ das sich nicht lagetrea in die Mengersche Universalkurve einbetten lasst”, Fundam. Math., 54:3 (1964), 251–258 | MR | Zbl

[3] H. Bothe, “Universalmengen bezüglich der Lage im $E^m$”, Fundam. Math., 56 (1965), 203–212 | MR

[4] D. R. McMillan, “Taming Cantor sets in $E^n$”, Bull. Amer. Math. Soc., 70:5 (1964), 706–708 | DOI | MR | Zbl

[5] M. A. Shtanko, “Vlozhenie kompaktov v evklidovo prostranstvo”, Matem. sb., 83 (125) (1970), 234–255

[6] H. Bothe, “Zur Lage null-and eindimensionaler Punktmengen im $E^3$”, Fundam. Math., 58 (1966), 16–30 | MR

[7] H. Bothe, “A Tangled $I$-Dimensional Continuum in $E^3$ which has the Cube-with-Handles Property”, Bull. Acad. Pol. Soc., 20:6 (1972), 481–486 | MR | Zbl

[8] J. L. Bryant, “On embeddings of compacta in Euclidean spase”, Proc Am. Math. Soc., 23:1 (1969), 46–51 | DOI | MR | Zbl

[9] J. L. Bryant, “On embeddings of $I$-dimensional compacta in $E^5$”, Duke Math. J., 38:2 (1971), 265–270 | DOI | MR | Zbl

[10] J. L. Bryant, “On embeddings with locally nice cross-sections”, Trans. Amer. Math. Soc., 155:2 (1971), 327–332 | DOI | MR | Zbl

[11] J. L. Bryant, D. W. Sumners, “On embeddings of $I$-dimensional compacta in a hyperplane in $E^4$”, Pacific J. Math., 33:3 (1970), 555–557 | MR | Zbl

[12] D. R. McMillan, H. Row, “Tangled embeddings of one-dimensional continua”, Proc. Amer. Math. Soc., 22 (1969), 378–385 | DOI | MR | Zbl

[13] W. R. Mason, “Homeomorphic continuous curves in 2-space are isotopic in 3-space”, Trans. Amer. Math. Soc., 142 (1969), 269–290 | DOI | MR | Zbl

[14] D. R. McMillan, “Non-planar embeddings of planar sets in $E^3$”, Fundam. Math., 84:3 (1974), 245–254 | MR | Zbl