메뉴 건너뛰기




Volumn 131, Issue 11, 2003, Pages 3463-3467

Whitney's example by way of Assouad's embedding

Author keywords

Assouad's embedding; Critical set; Van Koch snowflake; Whitney's example; Whitney's extension theorem

Indexed keywords


EID: 0142169081     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-03-06913-2     Document Type: Conference Paper
Times cited : (15)

References (21)
  • 1
    • 24544466960 scopus 로고
    • Thèse de Doctorat. Université de Paris XI, 91405 Orsay, France. MR 58:30989
    • P. Assouad, Espaces Métriques, Plongements, Facteurs, Thèse de Doctorat. Université de Paris XI, 91405 Orsay, France, 1977. MR 58:30989
    • (1977) Espaces Métriques, Plongements, Facteurs
    • Assouad, P.1
  • 5
    • 0034417211 scopus 로고    scopus 로고
    • Embeddings of Gromov hyperbolic spaces
    • MR 2001g:53077
    • M. Bonk and O. Schramm, Embeddings of Gromov hyperbolic spaces, Geom. Funct. Anal. 10 (2000), 266-306. MR 2001g:53077
    • (2000) Geom. Funct. Anal. , vol.10 , pp. 266-306
    • Bonk, M.1    Schramm, O.2
  • 6
    • 22844453615 scopus 로고    scopus 로고
    • Reifenberg flat metric spaces, snowballs, and embeddings
    • MR 2001c:49067
    • G. David and T. Toro, Reifenberg flat metric spaces, snowballs, and embeddings, Math. Ann. 315 (1999), 641-710. MR 2001c:49067
    • (1999) Math. Ann. , vol.315 , pp. 641-710
    • David, G.1    Toro, T.2
  • 7
    • 0142163516 scopus 로고
    • On the structure of level sets of differentiable mappings of an n-dimensional cube into a k-dimensional cube (Russian)
    • MR 20:942
    • A. Ya. Dubovickiǐ, On the structure of level sets of differentiable mappings of an n-dimensional cube into a k-dimensional cube (Russian), Izv. Akad. Nauk SSSR. Ser. Mat. 21 (1957), 371-418. MR 20:942
    • (1957) Izv. Akad. Nauk SSSR. Ser. Mat. , vol.21 , pp. 371-418
    • Dubovickiǐ, A.Ya.1
  • 8
    • 0003358442 scopus 로고
    • The geometry of fractal sets
    • Cambridge University Press, Cambridge. MR 88d:28001
    • K. J. Falconer, The geometry of fractal sets, Cambridge Tracts in Mathematics, 85. Cambridge University Press, Cambridge, 1986. MR 88d:28001
    • (1986) Cambridge Tracts in Mathematics , vol.85
    • Falconer, K.J.1
  • 10
    • 84963012322 scopus 로고
    • A dense arcwise connected set of critical points - Molehills out of mountains
    • MR 90f:26011
    • T. W. Körner, A dense arcwise connected set of critical points - molehills out of mountains, J. London Math. Soc. 38 (1988), 442-452. MR 90f:26011
    • (1988) J. London Math. Soc. , vol.38 , pp. 442-452
    • Körner, T.W.1
  • 11
    • 84966242200 scopus 로고
    • The degree of regularity of a quasiconformal mapping
    • MR 95a:30020
    • P. Koskala, The degree of regularity of a quasiconformal mapping, Proc. Amer. Math. Soc. 122 (1994), 769-772. MR 95a:30020
    • (1994) Proc. Amer. Math. Soc. , vol.122 , pp. 769-772
    • Koskala, P.1
  • 13
    • 84968510992 scopus 로고
    • A critical set with nonnull image has large Hausdorff dimension
    • MR 87i:26011
    • A. Norton, A critical set with nonnull image has large Hausdorff dimension, Trans. Amer. Math. Soc. 296 (1986), 367-376. MR 87i:26011
    • (1986) Trans. Amer. Math. Soc. , vol.296 , pp. 367-376
    • Norton, A.1
  • 14
    • 84966233431 scopus 로고
    • Functions not constant on fractal quasi-arcs of critical points
    • MR 89m:28013
    • A. Norton, Functions not constant on fractal quasi-arcs of critical points, Proc. Amer. Math. Soc. 106 (1989), 397-405. MR 89m:28013
    • (1989) Proc. Amer. Math. Soc. , vol.106 , pp. 397-405
    • Norton, A.1
  • 15
    • 0142194383 scopus 로고
    • Critical sets in the plane
    • MR 92f:57032
    • A. Norton and C. Pugh, Critical sets in the plane, Michigan Math. J. 38 (1991), 441-459. MR 92f:57032
    • (1991) Michigan Math. J. , vol.38 , pp. 441-459
    • Norton, A.1    Pugh, C.2
  • 17
    • 0142194384 scopus 로고
    • On the existence of functions having given partial derivatives on a curve
    • MR 16:344a
    • M. Sion, On the existence of functions having given partial derivatives on a curve, Trans. Amer. Math. Soc. 77 (1954), 179-201. MR 16:344a
    • (1954) Trans. Amer. Math. Soc. , vol.77 , pp. 179-201
    • Sion, M.1
  • 18
    • 0000398510 scopus 로고
    • A quasiconformal group not isomorphic to a Möbius group
    • MR 83b:30019
    • P. Tukia, A quasiconformal group not isomorphic to a Möbius group, Ann. Acad. Sci. Fenn. Ser. A I Math. 6 (1981), 149-160. MR 83b:30019
    • (1981) Ann. Acad. Sci. Fenn. Ser. A I Math. , vol.6 , pp. 149-160
    • Tukia, P.1
  • 19
    • 77956456169 scopus 로고
    • Analytic extensions of differentiable functions defined in closed sets
    • H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), 63-89.
    • (1934) Trans. Amer. Math. Soc. , vol.36 , pp. 63-89
    • Whitney, H.1
  • 20
    • 84972500348 scopus 로고
    • A function not constant on a connected set of critical points
    • H. Whitney, A function not constant on a connected set of critical points, Duke Math. J. 1 (1935), 514-517.
    • (1935) Duke Math. J. , vol.1 , pp. 514-517
    • Whitney, H.1
  • 21
    • 84968469737 scopus 로고
    • Surjective mappings whose differential is nowhere surjective
    • MR 91g:58025
    • Y. Yomdin, Surjective mappings whose differential is nowhere surjective, Proc. Amer. Math. Soc. 111 (1991), 267-270. MR 91g:58025
    • (1991) Proc. Amer. Math. Soc. , vol.111 , pp. 267-270
    • Yomdin, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.