Bulletin of the Belgian Mathematical Society - Simon Stevin

Topological Homotopy Groups

B. Mashayekhy, H. Ghane, Z. Hamed, and H. Mirebrahimi

Full-text: Open access

Abstract

D. K. Biss (Topology and its Applications 124 (2002) 355-371) introduced the topological fundamental group and presented some interesting basic properties of the notion. In this article we intend to extend the above notion to homotopy groups and try to prove some similar basic properties of the topological homotopy groups. We also study more on the topology of the topological homotopy groups in order to find necessary and sufficient conditions for which the topology is discrete. Moreover, we show that studying topological homotopy groups may be more useful than topological fundamental groups.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 3 (2008), 455-464.

Dates
First available in Project Euclid: 30 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1222783092

Digital Object Identifier
doi:10.36045/bbms/1222783092

Mathematical Reviews number (MathSciNet)
MR2457961

Zentralblatt MATH identifier
1155.55004

Subjects
Primary: 55Q05: Homotopy groups, general; sets of homotopy classes 55U40: Topological categories, foundations of homotopy theory 54H11: Topological groups [See also 22A05] 55P35: Loop spaces

Keywords
Topological fundamental group homotopy group $n$-semilocally simply connected

Citation

Ghane, H.; Hamed, Z.; Mashayekhy, B.; Mirebrahimi, H. Topological Homotopy Groups. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 3, 455--464. doi:10.36045/bbms/1222783092. https://projecteuclid.org/euclid.bbms/1222783092


Export citation