On monotonous separately continuous functions

Authors

  • Yaroslav I. Grushka Institute of Mathematics NAS of Ukraine

DOI:

https://doi.org/10.4995/agt.2019.9817

Keywords:

separately continuous mappings, linearly ordered topological spaces, Young's theorem

Abstract

Let T = (T, ≤) and T1= (T1 , ≤1) be linearly ordered sets and X be a topological space.  The main result of the paper is the following: If function ƒ(t,x) : T × X → T1 is continuous in each  variable (“t” and  “x”)  separately  and  function ƒx(t)  = ƒ(t,x) is  monotonous  on T for  every x ∈ X,  then ƒ is  continuous  mapping  from T × X to T1,  where T and T1 are  considered  as  topological  spaces  under  the order topology and T × X is considered as topological space under the Tychonoff topology on the Cartesian  product of topological spaces T and X.

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Author Biography

Yaroslav I. Grushka, Institute of Mathematics NAS of Ukraine

Department of Nonlinear analysis

References

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Published

2019-04-01

How to Cite

[1]
Y. I. Grushka, “On monotonous separately continuous functions”, Appl. Gen. Topol., vol. 20, no. 1, pp. 75–79, Apr. 2019.

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Articles