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   a note on cc(x) via a topological ring  
   
نویسنده mohamadian r. ,namdari m. ,najafian h. ,soltanpour s.
منبع journal of algebraic systems - 2023 - دوره : 10 - شماره : 2 - صفحه:323 -334
چکیده    Let cc(x) (resp., c ∗ c (x)) denote the functionally countable subalgebra of c(x) (resp., c∗ (x)), consisting of all functions (resp., bounded functions) with countable image. cc(x) (resp., c∗ c (x)) as a topological ring via mc-topology (resp.,m∗ c -topology) and uc-topology (resp., u ∗c -topology) is investigated and the equality of the latter two topologies is characterized. topological spaces which are called n-spaces are introduced andstudied. it is shown that the mc-topology on cc(x) and its relative topology as a subspace of c(x) (with m-topology) coincide if and only if x is an n-space. we also show that x is pseudocompact if and only if it is both a countably pseudocompact, and an n-space.
کلیدواژه functionally countable subalgebra; mc-topology; uc-topology; n-space.
آدرس shahid chamran university of ahvaz, department of mathematics, iran, shahid chamran university of ahvaz, department of mathematics, iran, shahid chamran university of ahvaz, department of mathematics, iran, petroleum university of technology, department of science, iran
پست الکترونیکی s.soltanpour@put.ac.ir
 
     
   
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