C(X) determines X - a unified theory





nearly realcompact, real maximal ideal, SRM ideal, realcompact, P-maximal ideal, P-compact space, structure space


One of the fundamental problem in rings of continuous function is to extract those spaces for which C(X) determines X, that is to  investigate X and Y such that C(X) isomorphic with C(Y ) implies X homeomorphic with Y. Later S. Banach and M. Stone proved independently with slight variance, that if X is compact Hausdorff space, C(X) also determine X. Their works were maximally extended by E. Hewitt by introducing realcompact spaces and later Melvin Henriksen and Biswajit Mitra solved the problem for locally compact and nearly realcompact spaces. In this paper we tried to develop a unified theory of this problem to cover up all the works in the literature introducing a notion called P-compact spaces.



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Author Biographies

Biswajit Mitra, The University of Burdwan

Department of Mathematics

Sanjib Das, The University of Burdwan

Department of Mathematics


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How to Cite

B. Mitra and S. Das, “C(X) determines X - a unified theory”, Appl. Gen. Topol., vol. 24, no. 1, pp. 83–93, Apr. 2023.



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