A Study of Function Spaces through a Functor

Dr. Pravanjan Kumar Rana

Abstract: Let X be a locally compact Hausdorff space and let Fn (X) = limit of the function spaces of maps of X into certain spaces of type K (, n) each of the spaces of sequences SPn, WSPn+1, WSPn+2,. . . , WSP n+m,. . . is a space of type K (, n), SPn WSPn+1 W2SPn+2. . . Wm SP n+m Wm+1SPn+m+1. . . . For any space X, we define the space Fn, m (X) = (Wm SPn+m) X topologized by the compact-open topology. The aim of this paper is i) to investigate the properties of Fn, m (X), ii) to study of the object Fn, m.

Keywords: Eilenberg-MacLane space, function spaces, -homotopy classes, contravariant functor, compact open topology

How to Cite?: Dr. Pravanjan Kumar Rana, "A Study of Function Spaces through a Functor", Volume 5 Issue 6, June 2016, International Journal of Science and Research (IJSR), Pages: 574-577, https://www.ijsr.net/getabstract.php?paperid=NOV164078, DOI: https://dx.doi.org/10.21275/NOV164078