Results 81 to 90 of about 383 (157)
A Short Study of Alexandroff Spaces
, 2007 In this paper, we discuss the basic properties of Alexandroff spaces. Several examples of Alexandroff spaces are given. We show how to construct new Alexandroff spaces from given ones. Finally, two invariants for compact Alexandroff spaces are defined and calculated for the given examples.
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Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces. [PDF]
J Appl Comput Topol, 2023 Lipiński M +3 more
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Orders, Alexandroff spaces and digraphs
, 2021 This thesis mainly deals with Alexandroff spaces which are related to some concepts like preorders, graphs and digraphs.The first chapter gives some basic notions about topology, order and minimal open sets, which are used in the next chapter.In the second chapter, Alexandroff spaces are defined by using minimal open sets, and definitions of preorder ...
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$g^\ast $-closed sets and a new separation axiom in Alexandroff spaces
, 2003 summary:In this paper we introduce the concept of $g^{\ast }$-closed sets and investigate some of its properties in the spaces considered by A. D. Alexandroff [1] where only countable unions of open sets are required to be open.
Rashid, Md. Mamun Ar, Das, Pratulananda
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Transversal and T1-independent topologies and the Alexandroff duplicate
, 2012 Two T1-topologies on a given set are called transversal if their union is a subbase for the discrete topology, and T1-independent if their intersection is the cofinite topology.
M. Tkachenko +3 more
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Extensions of topological spaces with strongly-discrete remainder
, 1999 The construction of the Alexandroff one-point compactification is extended to provide paracompact extensions of locally compact Hausdorff spaces with strongly-discrete ...
Collins, P.J.
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Closed graph property in Alexandroff spaces
In the following text we show if $X$ is an Alexandroff space, then $f:X\to Y$ has closed graph if and only if it has constant closed value on each connected component of $X$. Moreover, if $X$ an Alexandroff space and $f:X\to Y$ has closed graph, then $f:X\to Y$ is continuous.
Shirazi, Fatemah Ayatollah Zadeh +1 more
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On the Construction of Alexandroff Spaces
Alexandroff spaces, characterized by the property that arbitrary intersections of open sets remain open, play a fundamental role in topology and its applications. This article explores different methods for constructing Alexandroff spaces, organized into
MANCERO MOSQUERA, MARCELO ISAAC +1 more
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H-closed spaces and almost realcompact spaces
, 2023 It was P. Alexandroff and P. Urysohn who first introduced the class of H-closed spaces. Since then, it has evoked the interest of many topologists. The concept of H-closedness is closely related to that of compactness, and it is for this reason that ...
Halpin, Katherine
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Topological View of Flows Inside the BOLD Spontaneous Activity of the Human Brain. [PDF]
Front Comput Neurosci, 2020 Don APH, Peters JF, Ramanna S, Tozzi A.
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