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An example of a space whose all continuous mappings are almost injective

Pablo Mendoza Iturralde (2001)

Commentationes Mathematicae Universitatis Carolinae

We show that all continuous maps of a space X onto second countable spaces are pseudo-open if and only if every discrete family of nonempty G δ -subsets of X is finite. We also prove under CH that there exists a dense subspace X of the real line ℝ , such that every continuous map of X is almost injective and X cannot be represented as K ∪ Y , where K is compact and Y is countable. This partially answers a question of V.V. Tkachuk in [Tk]. We show that for a compact X , all continuous maps of X onto second...

An example of strongly self-homeomorphic dendrite not pointwise self-homeomorphic

Pavel Pyrih (1999)

Commentationes Mathematicae Universitatis Carolinae

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

Pavel Pyrih (1999)

Archivum Mathematicum

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 exotic flow on a compact surface

N. Markley, M. Vanderschoot (2000)

Colloquium Mathematicae

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 ο m e g a -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 2 with equally striking...

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