This article is cited in 3 papers

Structure of continuous functions of a completely regular space

V. V. Pashenkov

Moscow Engineering Building Institute

Abstract: It is proved that any completely regular topological space is determined up to homeomorphism by the topological lattice (with the topology of pointwise convergence) of all its continuous real-valued functions. The well-known result of Kaplansky (for compact spaces) is a corollary of this theorem.

UDC: 513.8

Received: 21.02.1974

 English version: Mathematical Notes, 1976, 19:6, 505–508

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