7 papers
Perfect maps between submetrizable spaces
Vlad Smolin
We investigate a question posed by Huaipeng Chen: if and are paracompact submetrizable spaces and is a perfect map, can and be submetrized by metrics …
Open images of spaces with a Lusin -base
Mikhail Patrakeev, Vlad Smolin
In [5] we studied spaces with a Lusin -base and -spaces and posed the following question: Does the class of continuous open images of spaces with a Lusin -base equal the c…
Closed and open-closed images of submetrizable spaces
Vlad Smolin
We prove that: 1. If a Hausdorff M-space is a continuous closed image of a submetrizable space, then it is metrizable. 2. A dense-in-itself open-closed image of a submetrizable spa…
Sequence-covering maps on submetrizable spaces
Vlad Smolin
A topological space is called a submetrizable if it can be mapped onto a metrizable topological space by a continuous one-to-one map. In this paper we answer two questions concerni…
-spaces and their open images
Mikhail Patrakeev, Vlad Smolin
We study spaces that can be mapped onto the Baire space (i.e. the countable power of the countable discrete space) by a continuous quasi-open bijection. We give a characterization…
A Hausdorff compact space is metrizable if and only if it is a continuous open image of the Sorgenfrey line
Vlad Smolin
In this note we prove that a regular continuous open image of the Sorgenfrey line with an uncountable weight has a closed subspace that is homeomorphic to the Sorgenfrey line. As a…
Open images of the Sorgenfrey line
Vlad Smolin
We give a description of Hausdorff continuous open images of the Sorgenfrey line: these are precisely those spaces that have a Sorgenfrey base. Using this description we prove that…