New Characterizations and Properties of Almost-open and Almost-closed Functions
No arc-connected treelike continuum is the 2-to-1 image of a continuum
In 1940, O. G. Harrold showed that no arc can be the exactly 2-to-1 continuous image of a metric continuum, and in 1947 W. H. Gottschalk showed that no dendrite is a 2-to-1 image. In 2003 we show that no arc-connected treelike continuum is the 2-to-1 image of a continuum.
Non-alternating mappings
Nonlinear contractive conditions: A comparison and related problems
We establish five theorems giving lists of nonlinear contractive conditions which turn out to be mutually equivalent. We derive them from some general lemmas concerning subsets of the plane which may be applied both in the single- or set-valued case as well as for a family of mappings. A separation theorem for concave functions is proved as an auxiliary result. Also, we discuss briefly the following problems for several classes of contractions: stability of procedure of successive approximations,...
Note on connections of the point of continuity property and Kuratowski problem on function having the Baire property
Notes on almost open mappings
Notes on -covers
The main purpose of this paper is to establish general conditions under which -spaces are compact-covering images of metric spaces by using the concept of -covers. We generalize a series of results on compact-covering open images and sequence-covering quotient images of metric spaces, and correct some mapping characterizations of -metrizable spaces by compact-covering -maps and -maps.
Notes on quotient maps
Nowhere dense sets and real-valued functions with closed graphs.
On a Class of Darboux Functions from a Topological Space to a Uniform Space
On a mixed-type interpolation problem for real polynomials
On a problem of Lelek concerning open mappings
On a theorem of Holický and Zelený concerning Borel maps without -compact fibers
The paper is concerned with a recent very interesting theorem obtained by Holický and Zelený. We provide an alternative proof avoiding games used by Holický and Zelený and give some generalizations to the case of set-valued mappings.
On a theorem of P. S. Aleksandrov
On almost continuity and expansion of open sets.
On almost precontinuous functions.
On almost quasicontinuous functions
A function is said to be almost quasicontinuous at if for each neighbourhood of . Some properties of these functions are investigated.
On an affirmative answer to Y. Tanaka's and Y. Ge's problem
In this paper, we give an affirmative answer to the problem posed by Y. Tanaka and Y. Ge (2006) in "Around quotient compact images of metric spaces, and symmetric spaces", Houston J. Math. 32 (2006) no. 1, 99-117.
On approximately semiopen maps in topological spaces.
On atomic mappings