Bulletin of the Belgian Mathematical Society - Simon Stevin

Topological Homotopy Groups

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

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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

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

First available in Project Euclid: 30 September 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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

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