On the hyperspaces of hereditarily indecomposable continua
On the hyperspaces of snake-like and circle-like continua
On the ideal convergence of sequences of quasi-continuous functions
For any Borel ideal ℐ we describe the ℐ-Baire system generated by the family of quasi-continuous real-valued functions. We characterize the Borel ideals ℐ for which the ideal and ordinary Baire systems coincide.
On the ideal (v 0)
The σ-ideal (v 0) is associated with the Silver forcing, see [5]. Also, it constitutes the family of all completely doughnut null sets, see [9]. We introduce segment topologies to state some resemblances of (v 0) to the family of Ramsey null sets. To describe add(v 0) we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen’s conjecture cov(v 0) = add(v 0) is confirmed under the hypothesis t = min{cf(c), r}. The hypothesis cov(v 0) = ω 1 implies that (v 0) has the ideal...
On the ideals of the semigroup of the 1-sphere
On the imbedding of extremally disconnected spaces into bicompacta
On the Index of Approximating Sets of Periodic Points.
On the inequivalence of the Borsuk and the H-shape theories for arbitrary metric spaces
On the insertion of Darboux functions
The main goal of this paper is to characterize the family of all functions f which satisfy the following condition: whenever g is a Darboux function and f < g on ℝ there is a Darboux function h such that f < h < g on ℝ.
On the intrinsic geometry of a unit vector field
We study the geometrical properties of a unit vector field on a Riemannian 2-manifold, considering the field as a local imbedding of the manifold into its tangent sphere bundle with the Sasaki metric. For the case of constant curvature , we give a description of the totally geodesic unit vector fields for and and prove a non-existence result for . We also found a family of vector fields on the hyperbolic 2-plane of curvature which generate foliations on with leaves of constant intrinsic...
On the inverse image of Baire spaces.
On the iterative process
On the iterative test for j-contractive mappings in uniform spaces
Edelstein iterative test for j-contractive mappings in uniform spaces is established.
On the -Baire property
In this note we show the following theorem: “Let be an almost -discrete space, where is a regular cardinal. Then is -Baire iff it is a -Baire space and every point- open cover of such that is locally- at a dense set of points.” For we obtain a well-known characterization of Baire spaces. The case is also discussed.
On the lattice of convexly compatible topologies on a partially ordered set
On the lattice of topologies
On the lattice structure of topologies
On the LC1-spaces which are Cantor or arcwise homogeneous
A space X containing a Cantor set (an arc) is Cantor (arcwise) homogeneousiff for any two Cantor sets (arcs) A,B ⊂ X there is an autohomeomorphism h of X such that h(A)=B. It is proved that a continuum (an arcwise connected continuum) X such that either dim X=1 or is Cantor (arcwise) homogeneous iff X is a closed manifold of dimension at most 2.
On the Lefschetz fixed point theorem
On the Lefschetz fixed point theorem for multivalued weighted mappings