On thick spaces
On thin-tall scattered spaces
On tho existence of weak P-points in compact F-spaces
On three equivalences concerning Ponomarev-systems
Let be a sequence of covers of a space such that is a network at in for each . For each , let and be endowed the discrete topology. Put forms a network at some point and by choosing for each . In this paper, we prove that is a sequentially-quotient (resp. sequence-covering, compact-covering) mapping if and only if each is a -cover (resp. -cover, -cover) of . As a consequence of this result, we prove that is a sequentially-quotient, -mapping if and only if it is...
On tightness in chain-net spaces
On time reparametrizations and isomorphisms of impulsive dynamical systems
We prove that for a given impulsive dynamical system there exists an isomorphism of the basic dynamical system such that in the new system equipped with the same impulse function each impulsive trajectory is global, i.e. the resulting dynamics is defined for all positive times. We also prove that for a given impulsive system it is possible to change the topology in the phase space so that we may consider the system as a semidynamical system (without impulses).
On top spaces.
On topological and algebraic structure of extremally disconnected semitopological groups
Starting with a very simple proof of Frol’ık’s theorem on homeomorphisms of extremally disconnected spaces, we show how this theorem implies a well known result of Malychin: that every extremally disconnected topological group contains an open and closed subgroup, consisting of elements of order . We also apply Frol’ık’s theorem to obtain some further theorems on the structure of extremally disconnected topological groups and of semitopological groups with continuous inverse. In particular, every...
On topological entropy
On topological ergodic measure spaces.
On topological factors of 3 dimensional locally connected continuum embeddable in
On topological groups with a small base and metrizability
A (Hausdorff) topological group is said to have a -base if it admits a base of neighbourhoods of the unit, , such that whenever β ≤ α for all . The class of all metrizable topological groups is a proper subclass of the class of all topological groups having a -base. We prove that a topological group is metrizable iff it is Fréchet-Urysohn and has a -base. We also show that any precompact set in a topological group is metrizable, and hence G is strictly angelic. We deduce from this result...
On topological properties of the spaces of Darboux Baire 1 functions and bounded derivatives
We investigate the topological structure of the space 𝓓ℬ₁ of bounded Darboux Baire 1 functions on [0,1] with the metric of uniform convergence and with the p*-topology. We also investigate some properties of the set Δ of bounded derivatives.
On Topological Spaces With Dense Completely Metrizable Subspaces
On topological types of the simplest indecomposable continua
On topologies convexly compatible with the ordering
On topologies generated by some operators
The paper concerns topologies introduced in a topological space (X, τ) by operators which are much weaker than the lower density operators. Some properties of the family of sets having the Baire property and the family of meager sets with respect to such topologies are investigated.
On topologies generating the Effros Borel structure and on the Effros measurability of the boundary operation
On topologies of free groups
On total orderings in topology