Almost continuous multifunctions
Almost contra-precontinuous functions.
Almost every function is independent
Almost -closed functions and separation axioms
We introduce a new class of functions called almost -closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost -closed continuous surjections.
Almost lower semicontinuous multifunctions and the Souslin-graph theorem
Almost midconvex and almost convex set-valued functions
Almost nearly continuous multifunctions.
Almost quasicontinuity of multivalued maps on product spaces
Almost -continuous functions.
Almost -precontinuous multifunctions.
Almost-continuous path connected spaces.
Almost-Homeomorphisms And Almost-Topological Properties.
Always of the first category sets
Always of the first category sets (II)
An abstract version of Sierpiński's theorem and the algebra generated by A and CA functions
We give an abstract version of Sierpiński's theorem which says that the closure in the uniform convergence topology of the algebra spanned by the sums of lower and upper semicontinuous functions is the class of all Baire 1 functions. Later we show that a natural generalization of Sierpiński's result for the uniform closure of the space of all sums of A and CA functions is not true. Namely we show that the uniform closure of the space of all sums of A and CA functions is a proper subclass of the...
An algebraic and logical approach to continuous images
An Alternative Theorem for Continuous Relations and its Applications
An answer to a question of Arhangel'skii
We prove that there exists an example of a metrizable non-discrete space , such that but where and is the space of all continuous functions from into reals equipped with the topology of pointwise convergence. It answers a question of Arhangel’skii ([2, Problem 4]).
An answer to a question of Cao, Reilly and Xiong
We present a simple proof of a Banach-Stone type Theorem. The method used in the proof also provides an answer to a conjecture of Cao, Reilly and Xiong.
An Application of the Stiefel-Whitney Classes to the Proof of a Fixed Point Theorem for Set-Valued Mappings
We prove a fixed point theorem for Borsuk continuous mappings with spherical values, which extends a previous result. We apply some nonstandard properties of the Stiefel-Whitney classes.