The topologization of the space of separately continuous functions

Authors

  • 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

DOI:

https://doi.org/10.15330/cmp.5.2.199-207

Keywords:

separately continuous functions, polynomials of two variables, topology of the layer uniform convergence, completeness, Hausdorff property, metrizability, separability

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.

Additional Files

Published

2013-12-30

How to Cite

(1)
Voloshyn, H.; Maslyuchenko, V. The Topologization of the Space of Separately Continuous Functions. Carpathian Math. Publ. 2013, 5, 199-207.

Issue

Section

Scientific articles