Geodesic
Approximation of compacta in $E^n$ in codimension greater than two
Sbornik. Mathematics, Tome 19 (1973) no. 4, pp. 615-626 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The following is proved. Theorem. For a compactum of codimension greater than or equal to three lying in Euclidean space there exists an arbitrarily close approximation by a locally homotopically unknotted (1-ULC) imbedding. A series of corollaries about approximation of imbeddings of manifolds and polyhedra is derived. A problem about Menger universal compacta is solved. The article contains the complete proof of previously announced results stated in the references. Bibliography: 17 titles. 
@article{SM_1973_19_4_a6,
     author = {M. A. Shtan'ko},
     title = {Approximation of compacta in $E^n$ in codimension greater than two},
     journal = {Sbornik. Mathematics},
     pages = {615--626},
     year = {1973},
     volume = {19},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_19_4_a6/}
}
TY  - JOUR
AU  - M. A. Shtan'ko
TI  - Approximation of compacta in $E^n$ in codimension greater than two
JO  - Sbornik. Mathematics
PY  - 1973
SP  - 615
EP  - 626
VL  - 19
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1973_19_4_a6/
LA  - en
ID  - SM_1973_19_4_a6
ER  - 
%0 Journal Article
%A M. A. Shtan'ko
%T Approximation of compacta in $E^n$ in codimension greater than two
%J Sbornik. Mathematics
%D 1973
%P 615-626
%V 19
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1973_19_4_a6/
%G en
%F SM_1973_19_4_a6
M. A. Shtan'ko. Approximation of compacta in $E^n$ in codimension greater than two. Sbornik. Mathematics, Tome 19 (1973) no. 4, pp. 615-626. http://geodesic.mathdoc.fr/item/SM_1973_19_4_a6/

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

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

[3] J. L. Bryant, C. L. Seebeck, “Locally nice embeddings in codimension three”, Quart. J. Math., 21 (1970), 265–272 | DOI | MR | Zbl

[4] J. I. Cobb, “Taming almost $PL$ embeddings in codimension 3”, Notices Amer. Math. Soc., 15:2 (1968), 371

[5] A. V. Chernavskii, “Topologicheskie vlozheniya mnogoobrazii”, DAN SSSR, 187:6 (1969), 1247–1249

[6] J. L. Bryant, C. L. Seebeck, “Locally nice embeddings in codimension three”, Bull. Amer. Math. Soc., 74 (1968), 378–380 | DOI | MR | Zbl

[7] A. V. Chernavskii, “Kusochno lineinaya approksimatsiya vlozhenii mnogoobrazii v korazmernostyakh, bolshikh dvukh”, Matem. sb., 82 (124) (1970), 499–500

[8] R. T. Miller, “Approximating codimension 3 embeddings”, Ann. Math., 95:3 (1972), 406–416 | DOI | MR | Zbl

[9] T. B. Rushing, “Locally flat embeddings of $PL$ manifolds are $\varepsilon$-tame in codimension three”, Top. Manif. Proc. Univ. Georgia, 1969 | MR

[10] R. C. Kirby, L. C. Siebenmann, C. T. C. Wall, “The annulus conjecture and triangulation”, Notices Amer. Math. Soc., 16 (1969), 432

[11] M. A. Shtanko, “Reshenie zadachi Mengera v klasse kompaktov”, DAN SSSR, 201:6 (1971), 1299–1302

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

[13] P. S. Aleksandrov, Kombinatornaya topologiya, Gostekhizdat, Moskva, 1947 | MR

[14] V. Gurevich, G. Volmen, Teoriya razmernosti, IL, Moskva, 1948

[15] P. S. Aleksandrov, “O razmernosti zamknutykh mnozhestv”, Uspekhi matem. nauk, IV:6 (34) (1949), 17–88

[16] G. Zeifert, V. Trellfall, Topologiya, GONTI, Moskva, 1938

[17] M. A. Shtanko, “Approksimatsiya vlozheniya kompaktov v korazmernosti, bolshei dvukh”, DAN SSSR, 198:1 (1971), 783–786