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Topological Properties of Quasilinear Spaces and Set-Valued Maps

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  • Sanjay Kumar Suman

    (Department of Mathematics, Government Degree College, Bagaha, West Champaran, B.R.A. Bihar University, Muzaffarpur, Bihar, India.)

Abstract

This paper presents a comprehensive study on the topological properties within the framework of quasilinear spaces, particularly focusing on their application to set-valued maps. We generalize the established concept of normed quasilinear spaces, primarily as introduced by Aseev in 1986, to the more encompassing notion of topological quasilinear spaces1. Our investigation demonstrates that if S is an arbitrary topological space and Z is a metrizable topological vector space, then the space of minimal semi-continuous compact-valued maps, denoted as M(S,Y), can be mapped into a linear space. This significantly extends previous results where S was restricted to being a Baire space.

Suggested Citation

  • Sanjay Kumar Suman, 2025. "Topological Properties of Quasilinear Spaces and Set-Valued Maps," International Journal of Research and Scientific Innovation, International Journal of Research and Scientific Innovation (IJRSI), vol. 12(6), pages 2162-2174, June.
    • Handle: RePEc:bjc:journl:v:12:y:2025:i:6:p:2162-2174
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