Fixed Point Set and Equivariant Map of a S-Topological Transformation Group

Rajapandiyan, C.; Visalakshi, V.

doi:10.28924/2291-8639-22-2024-20

Research Article

Fixed Point Set and Equivariant Map of a S-Topological Transformation Group

C. Rajapandiyan
V. Visalakshi*

* Corresponding author

Abstract

The fixed point set and equivariant map of a S-topological transformation group is explored in this work. For any subset K of G, it is established that the fixed point set X^K is clopen in X and for a free S-topological transformation group, it is proved that the fixed point set of K is equal to the fixed point set of closure and interior of the subgroup of G generated by K. Subsequently, it is proved that the map between STC_G(X) and STC_G’(X’) is a homomorphism under a Φ’- equivariant map. Also, it is proved that there is an isomorphism between the quotient topological groups and some basic properties of fixed point set of a S-topological transformation group are studied.

How to Cite

C. Rajapandiyan, V. Visalakshi, Fixed Point Set and Equivariant Map of a S-Topological Transformation Group, Int. J. Anal. Appl. 22 (2024), 20. https://doi.org/10.28924/2291-8639-22-2024-20

BibTeX

@article{Rajapandiyan2024,
  author  = {Rajapandiyan, C. and Visalakshi, V.},
  title   = {Fixed Point Set and Equivariant Map of a S-Topological Transformation Group},
  journal = {Int. J. Anal. Appl.},
  volume  = {22},
  year    = {2024},
  pages   = {20},
  doi     = {10.28924/2291-8639-22-2024-20}
}

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