Related papers: Open images of spaces with a Lusin $\pi$-base
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 of such spaces in terms of Souslin schemes and call these…
We give descriptions of metrizable topological spaces that are images of the Sorgenfrey line under continuous maps of different types (open, closed, quotient and others). To obtain this descriptions, we introduce the notion of a Lusin…
We construct a space ${X}$ that has a Lusin $\pi$-base and such that ${X}^{2}$ has no Lusin $\pi$-base.
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 no Hausdorff compact space that contains a copy of the…
A space $X$ is said to be $\pi$-metrizable if it has a $\sigma$-discrete $\pi$-base. In this paper, we mainly give affirmative answers for two questions about $\pi$-metrizable spaces. The main results are that: (1) A space $X$ is…
We prove that the category of c-spaces with continuous maps is not cartesian closed. As a corollary the category of locally finitary compact spaces with continuous maps is also not cartesian closed.
A Lusin space is a Hausdorff space being the image of a Polish space under a continuous bijection. Such spaces have multiple applications, in particular, as state spaces of various stochastic systems. In this work, we consider the spaces…
A topological space is $Suslin$ ($Lusin$) if it is a continuous (and bijective) image of a Polish space. For a Tychonoff space $X$ let $C_p(X)$, $C_k(X)$ and $C_{{\downarrow}F}(X)$ be the space of continuous real-valued functions on $X$,…
Similar to the definition of Dupin hypersurface in Riemannian space forms, we define the spacelike Dupin hypersurface in Lorentzian space forms. As conformal invariant objects, spacelike Dupin hypersurfaces are studied in this paper using…
In view of the fact that many of the most familiar examples of category bases are equivalent to some topology, it is natural to ask whether category bases are always topological in nature. The answer is in the negative. In this paper, we…
In this paper, the authors mainly discuss the images of spaces with an uniform base at non-isolated points, and obtain the following main results: (1)\ Perfect maps preserve spaces with an uniform base at non-isolated points; (2)\ Open and…
The class of Hausdorff spaces that are continuous images of compact orderable spaces is studied by analyzing the relationship between the elements of this class and compact orderable spaces in a back-and-forth fashion. Structure results for…
In this paper,\ the authors define a space with an uniform base at non-isolated points, give some characterizations of images of metric spaces by boundary-compact maps, and study certain relationship among spaces with special base…
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.
Contrastive Language-Image Pre-training (CLIP) formulates image classification as an image-to-text matching task, i.e., matching images to the corresponding natural language descriptions instead of discrete category IDs. This allows for…
We study the existence of non-separable compact spaces that support a measure and are small from the topological point of view. In particular, we show that under Martin's axiom there is a non-separable compact space supporting a measure…
In this paper, the authors construct some counterexamples to show that the generalized Carleson measure space and the Triebel-Lizorkin-type space are not equivalent for certain parameters, which was claimed to be true in [Taiwanese J. Math.…
For $C^0$ generic continuous maps or homeomorphisms on compact Riemannian manifold, we prove that (1) the space of physical-like measures coincides with the set of invariant measures supported on chain recurrent classes, (2) every point in…
We report results on the scaling properties of changes in contrast of natural images in different visual environments. This study confirms the existence, in a vast class of images, of a multiplicative process relating the variations in…
We investigate the class of continuous images of non-commutative Valdivia compact spaces, in particular its subclass of weakly non-commutative Cor- son countably compact spaces. A key tool is the study of non-commutative Corson countably…