On the pseudo-interior of Menger sponge

Authors

  • Vladimir Todorov University of Architecture, Civil Engineering and Geodesy, Sofia, Bulgaria

Keywords:

Menger sponge, pseudo interior, N¨obeling space

Abstract

It is proven in [1] that the pseudo-interior of the Menger universal space µ^1 is homeomorphic to the N¨obeling space N^3_1 . Note that a complete description of topological properties of µ^1 and N^3_1 in [1] is given. This note contains a simple proof that the
pseudo interior of µ^1 and N^3_1 are homeomorphic.

Author Biography

Vladimir Todorov, University of Architecture, Civil Engineering and Geodesy, Sofia, Bulgaria

UACG
1, Hristo Smirnenski Blvd
1046 Sofia, Bulgaria

References

K. Kawamura, M. Levin, E. D. Tymchatyn. A characterization of 1-dimensional Nobeling spaces. Proceedings of the 12th Summer Conference on General Topology and its Applications (North Bay, ON, 1997). Topology Proc. 22, Summer (1997), 155-174.

W. Sierpinski. ´ Sur une courbe cantorienne qui contient une image biunivoque et continue de toute courbe donn´ee. C. R. Acad. Sci. Paris. 162 (1916), 629–632 (in French).

P. S. Aleksandrov, B. A. Pasynkov. Vvedeniye v teoriyu razmernosti: Vvedeniye v teoriyu topologicheskikh prostranstv i obshchuyu teoriyu razmernosti. Moskva, Nauka, 1973 (in Russian) [Introduction to dimension theory: An introduction to the theory of topological spaces and the general theory of dimension. Moscow, Nauka, 1973.]

C. Bessaga, A. Pelczynski. ´ Selected topics in infinite-dimensional topology. Monografie Matematyczne, tom 58. [Mathematical Monographs, Vol. 58] Warsaw, PWN – Polish Scientific Publishers, 1975.

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Published

2022-04-01

How to Cite

[1]
Todorov, V. 2022. On the pseudo-interior of Menger sponge. Mathematics and Education in Mathematics. 51, (Apr. 2022), 139–144.

Issue

Section

Section A: Mathematical Structures