We characterize normal and extremally disconnected biframes in terms of the insertion of a continuous real function in between given lower and upper semicontinuous real functions and show this to be the common root of several classical and new insertion results concerning topological spaces, bitopological spaces, ordered topological spaces and locales.

In this paper, we study MV?algebra of continuous functions C(X) and maximal ideals C(X). Furthermore, Z?ideal Z??ideal are introduced proved that every in is a but the converse not true finitely generated basic Z??ideal. Also, investigate meet join two Z?ideals (Z??ideal) Complemented elements examined their properties have been studied. particular, relationship between ideal by them (Z??ideals...

The purpose of the present article is to introduce notion (Λ, s)-closed sets. Especially, some properties generalized sets are obtained. Several characterizations low separation axioms given. Characterizations s)-extremally disconnected spaces investigated. Furthermore, almost s)-continuous functions discussed.

In this paper, we study the class of generalized b-closed sets and use this notion to consider new weak and stronger forms of continuities associated with these sets. We apply these notions to give new characterization of extremally disconnected spaces and also Tgs-spaces. 2000 Mathematics Subject Classification: 54A10, 54C8, 54C10, 54D10

In this article I will analyze the impact of forcing with a measure algebra on various topological statements. In particular our interest will focus on the study of hereditary separability and the hereditary Lindelöf property in the classes of compact, extremally disconnected, and cometrizable spaces.