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TOPOLOGICAL R2-DIVISIBLE R3-SPACES

  • Im, Jang-Hwan (Graduate School of Advanced Imaging Science Multimedia, and Film, Chung-Ang University)
  • Published : 2002.10.01

Abstract

There are many models to study topological $R^2$-planes. Unlike topological $R^2$-planes, it is difficult to find models to study topological R$^3$)-spaces. If an 4-dimensional affine plane intersects with R$^3$, we are able to get a geometrical structure on R$^3$ which is similar to R$^3$-space, and called $R^2$-divisible R$^3$-space. Such spatial geometric models is useful to study topological R$^3$-spaces. Hence, we introduce some classes of topological $R^2$-divisible R$^3$-spaces which are induced from 4-dimensional anne planes.

Keywords

topological geometry;spatial gemetry

References

  1. Resultate der Math v.6 Einbettung von topologischen Raumgeometrien auf R³ in den reellen affinen Raun D. Betten;C. Horstmann
  2. Dissertation Topologische Differenzenfichenebenen mit nichtkommutativer Stand-gruppe N. Knarr
  3. Math. Z. v.121 Kollineationsgruppen kompakter 4-dimensiionaler Ebenen https://doi.org/10.1007/BF01113480
  4. 4-dimensional compact projective planes of orbit type(1,1) D. Betten;B. Polster
  5. Singular Homology Theory W.S. Massey
  6. Note di Matematica v.15 no.2 A class of topological space geometries J.-H. Im
  7. Simon Stevin v.55 Topologische Geometrien auf 3-Mannigfaltigkeiten D. Betten
  8. Abh. Math. Sem. Ham-burg v.28 Zur Klassifikation topologischer Ebenen III H. Salzmann https://doi.org/10.1007/BF02993254
  9. Dissertation Continuous planar functions B. Polster
  10. Adv. in Math v.2 Topological planes https://doi.org/10.1016/S0001-8708(67)80002-1
  11. Compact Projective Planes, De Gruyter H. Salzmann
  12. Geom. Ded v.16 4-dimensionale projective Ebenen mit 3-dimensionaler Translations-gruppe
  13. Math. Z. v.117 Kollineationsgruppen kompakter vier-dimensionaler Ebenen https://doi.org/10.1007/BF01109833
  14. Atti. Sem. Mat. Fis. Modena v.24 Flexible Reumgeometrien
  15. Resultate der Math v.12 Einige Klassen topologischer 3-Rame https://doi.org/10.1007/BF03322377
  16. The geometry of geodesics H. Busemann