The topologization of the space of separately continuous functions

  • H.A. Voloshyn Bukovinian State Financial and Economics University, 1 Stern str., 58000, Chernivtsi, Ukraine
  • V.K. Maslyuchenko Yuriy Fedkovych Chernivtsi National University, 2 Kotsjubynskyi str., 58012, Chernivtsi, Ukraine
Keywords: separately continuous functions, polynomials of two variables, topology of the layer uniform convergence, completeness, Hausdorff property, metrizability, separability
Published online: 2013-12-30

Abstract


Here we introduce locally convex topology $\mathcal{T}$ of the layer uniform convergence on the space $ S = CC [0,1] ^ 2 $ of all separately continuous functions $ f: [0,1] ^ 2 \rightarrow \mathbb{R}$, we prove that the space $(S, \mathcal{T}) $ is complete and it is not metrizable one, the space $ P $ of all polynomials of two variables on $ [0,1] ^ 2 $ is everywhere dense in $ S $, and so, $ S $ is separable.
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How to Cite
(1)
VoloshynH., MaslyuchenkoV. The Topologization of the Space of Separately Continuous Functions. Carpathian Math. Publ. 2013, 5 (2), 199-207.