We investigate the relations between decreasing sequences of sets and the insertion of semi-continuous functions, and give
some characterizations of countably metacompact spaces, countably paracompact spaces, monotonically countably paracompact
spaces (MCP), monotonically countably metacompact spaces (MCM), perfectly normal spaces and stratifiable spaces.
whereAt is a multivaluedm-accretive operator on a Banach spaceE andF is a measurable multifunction defined on the set
, lower semicontinuous inx and its values are not necessarily convex inE. This result generalizes some results in  and .
In , Dlaska introduced the class of almost rc-Lindelf sets and studied some basic properties of such sets. In this paper,
we obtain further results concerning almost rc-Lindelf sets. We also introduce new concepts to obtain several mapping properties
concerning almost rc-Lindelf sets and almost rc-Lindelf spaces. The property of being an almost rc-Lindelf set is invariant
under functions which are slightly continuous and weakly θ-irresolute. It is also shown that the property of being an almost
rc-Lindelf space is inverse invariant under functions which are weakly almost open, ω-regular open, and whose fibers are
Extremal disconnectedness is further investigated for generalized topological spaces. It is found that extremally disconnected generalized topological spaces are a rich source of generalized lower semi-continuous and generalized upper semi-continuous mappings.
The following two theorems are obtained. (1) A mapping fis A-continuous if and only if it is semi-continuous and C-continuous. (2) A mapping f is A-continuous if and only if it is spr-continuous and LC-continuous.
The following two decomposition theorems are obtained. (1) A function f is α-continuous if and only if f is pre-continuous and αα-continuous, (2) A function f is semi-continuous if and only if f is spr-continuous and αLC-continuous.