An Example of a Q-minimal Precompact Topological Group Containing a Nonminimal Closed Normal Subgroup.
An example of a space whose all continuous mappings are almost injective
We show that all continuous maps of a space onto second countable spaces are pseudo-open if and only if every discrete family of nonempty -subsets of is finite. We also prove under CH that there exists a dense subspace of the real line , such that every continuous map of is almost injective and cannot be represented as , where is compact and is countable. This partially answers a question of V.V. Tkachuk in [Tk]. We show that for a compact , all continuous maps of onto second...
An example of a Ф-algebra whose uniform closure is a ring of continuous functions
An example of infinitely many sinks for smooth interval maps.
An example of maximal connected Hausdorff space
An example of semilinear topologies.
An example of strongly self-homeomorphic dendrite not pointwise self-homeomorphic
Such spaces in which a homeomorphic image of the whole space can be found in every open set are called self-homeomorphic. W.J. Charatonik and A. Dilks asked if any strongly self-homeomorphic dendrite is pointwise self-homeomorphic. We give a negative answer in Example 2.1.
An example related to strongly pointwise self-homeomorphic dendrites
Such spaces in which a homeomorphic image of the whole space can be found in every open set are called self-homeomorphic. W.J. Charatonik and A. Dilks posed a problem related to strongly pointwise self-homeomorphic dendrites. We solve this problem negatively in Example 2.1.
An exchange theorem for infinite sums and limits in Banach spaces.
An existence theorem via an intuitive idea and fixed-point theorems
An exotic flow on a compact surface
In 1988 Anosov [1] published the construction of an example of a flow (continuous real action) on a cylinder or annulus with a phase portrait strikingly different from our normal experience. It contains orbits whose -limit sets contain a non-periodic orbit along with a simple closed curve of fixed points, but these orbits do not wrap down on this simple closed curve in the usual way. In this paper we modify some of Anosov’s methods to construct a flow on a surface of genus with equally striking...
An extension of A. Ostrowski's Theorem on the round-off stability of iterations.
An extension of Edelstein's theorem to a uniform space.
An extension of Gregus fixed point theorem.
An extension of Kirk-Schöneberg theorem to uniform spaces
An extension of Kirk - Schöneberg surjectivity result is established.
An extension of the Stone representation for orthomodular lattices
An extension theorem for continuous functions
An extension theorem for multifunctions and a characterization of complete metric spaces
An extension theorem for separately continuous functions and its application to functional analysis
An extension theorem for sober spaces and the Goldman topology.