The fundamental group of the space $\Omega_n(m)$
| Autor: | A.M. Pasko |
|---|---|
| Jazyk: | English<br />Ukrainian |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Researches in Mathematics, Vol 30, Iss 1, Pp 66-70 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2664-4991 2664-5009 |
| DOI: | 10.15421/242207 |
| Popis: | In the present paper the spaces $\Omega_n(m)$ are considered. The spaces $\Omega_n(m)$, introduced in 2018 by A.M. Pasko and Y.O. Orekhova, are the generalization of the spaces $\Omega_n$ (the space $\Omega_n(2)$ coincides with $\Omega_n$). The investigation of homotopy properties of the spaces $\Omega_n$ has been started by V.I. Ruban in 1985 and followed by V.A. Koshcheev, A.M. Pasko. In particular V.A. Koshcheev has proved that the spaces $\Omega_n$ are simply connected. We generalized this result proving that all the spaces $\Omega_n(m)$ are simply connected. In order to prove the simply connectedness of the space $\Omega_n(m)$ we consider the 1-skeleton of this space. Using 1-cells we form the closed ways that create the fundamental group of the space $\Omega_n(m)$. Using 2-cells we show that all these closed ways are equivalent to the trivial way. So the fundamental group of the space $\Omega_n(m)$ is trivial and the space $\Omega_n(m)$ is simply connected. |
| Databáze: | Directory of Open Access Journals |
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