Function Spaces and Points in Čech-Stone Remainders

Let X and Y be locally compact normal spaces and let u is an element of X* and v is an element of Y*. In this paper we will show that if X-u and Y-v are lp-equivalent then u is omega-near if and only if v is. This result does not necessarily hold for spaces that are not locally compact. We will also show for locally compact normal spaces X and Y, that if u is an element of X* and v is an element of Y* are omega-near and X-u and Y-v are l(p)-equivalent, then omega((u) over cap) and omega((v) over cap) are homeomorphic for some 'unique' (u) over cap, (v) over cap is an element of omega* 'good' for u and v. These results allow us to find an isomorphic classification of function spaces C-p(alpha(u)), where alpha < omega(omega) is a limit ordinal and u is an element of alpha*. This extends a result due to Gul'ko for alpha = omega. We will also indicate that the proof for this isomorphic classification can only partly be extended for alpha >= omega(omega). (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.