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Strongly fixed ideals in C ( L ) and compact frames

A. A. EstajiA. Karimi FeizabadiM. Abedi — 2015

Archivum Mathematicum

Let C ( L ) be the ring of real-valued continuous functions on a frame L . In this paper, strongly fixed ideals and characterization of maximal ideals of C ( L ) which is used with strongly fixed are introduced. In the case of weakly spatial frames this characterization is equivalent to the compactness of frames. Besides, the relation of the two concepts, fixed and strongly fixed ideals of C ( L ) , is studied particularly in the case of weakly spatial frames. The concept of weakly spatiality is actually weaker than...

Locally functionally countable subalgebra of ( L )

M. ElyasiAA. EstajiM. Robat Sarpoushi — 2020

Archivum Mathematicum

Let L c ( X ) = { f C ( X ) : C f ¯ = X } , where C f is the union of all open subsets U X such that | f ( U ) | 0 . In this paper, we present a pointfree topology version of L c ( X ) , named c ( L ) . We observe that c ( L ) enjoys most of the important properties shared by ( L ) and c ( L ) , where c ( L ) is the pointfree version of all continuous functions of C ( X ) with countable image. The interrelation between ( L ) , c ( L ) , and c ( L ) is examined. We show that L c ( X ) c ( 𝔒 ( X ) ) for any space X . Frames L for which c ( L ) = ( L ) are characterized.

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