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pro vyhledávání: '"54F65"'
In this note, we present two pairs of conic-line arrangements admitting a unique conic and that form Zariski pairs, both of degree $9$. Their topologies are distinguished using the connected numbers.
Comment: 7 pages, 2 figures
Comment: 7 pages, 2 figures
Externí odkaz:
http://arxiv.org/abs/2410.04969
Autor:
İzci, Bilge, Özkoç, Murad
The aim of this paper is to introduce the notion of $a$-locally closed set by utilizing $a$-open sets defined by Ekici and to study some properties of this new notion. Also, some characterizations and many fundamental results regarding this new conce
Externí odkaz:
http://arxiv.org/abs/2408.03169
Autor:
Goswami, Amartya
We prove that the set of proper ideals of a monoid endowed with coarse lower topology is a spectral space.
Externí odkaz:
http://arxiv.org/abs/2407.04644
Autor:
de Souza, Lucas H. R.
Here we classify all topological spaces where all bijections to itself are homeomorphisms. As a consequence, we also classify all topological spaces where all maps to itself are continuous. Analogously, we classify all measurable spaces where all bij
Externí odkaz:
http://arxiv.org/abs/2401.04381
Motivated by results of J. R. Kline and R. L. Moore (1919) that a compact subset of the plane, homeomorphic to a subset of the reals, lies on the arc, we give a purely topological characterisation of compact sets of the reals. This allows us to reduc
Externí odkaz:
http://arxiv.org/abs/2312.13047
Autor:
Kula, Mateusz, Nowakowski, Piotr
We examine properties of achievement sets of series in $\mathbb{R}^2$. We show several examples of unusual sets of subsums on the plane. We prove that we can obtain any set of P-sums as a cut of an achievement set in $\mathbb{R}^2.$ We introduce a no
Externí odkaz:
http://arxiv.org/abs/2312.08155
Autor:
Gutev, Valentin
In 1951, Ernest Michael wrote a definitive seminal article on hyperspaces raising a general question that became known as the hyperspace selection problem. The present paper contains some aspects of this problem, along with several open questions. Mo
Externí odkaz:
http://arxiv.org/abs/2310.19085
We study the properties of topological spaces $(X,\tau)$, where $X$ is a definable set in an o-minimal structure and the topology $\tau$ on $X$ has a basis that is (uniformly) definable. Examples of such spaces include the canonical euclidean topolog
Externí odkaz:
http://arxiv.org/abs/2310.04510
Autor:
Goswami, Amartya
The purpose of this note is a wide generalization of the topological results of various classes of ideals of rings, semirings, and modules, endowed with Zariski topologies, to strongly irreducible ideals (endowed with Zariski topologies) of monoids,
Externí odkaz:
http://arxiv.org/abs/2304.11746
Autor:
Goswami, Amartya
We study the topology of a class of proper submodules and some of its distinguished subclasses and call them structure spaces. We give several criteria for the quasi-compactness of these structure spaces. We study $T_0$ and $T_1$ separation propertie
Externí odkaz:
http://arxiv.org/abs/2304.07692