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Fractal Topological Analysis for 2D Binary Digital Images
Fractal dimension is a powerful tool employed as a measurement of geometric aspects. In this work we propose a method of topological fractal analysis...
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Weakly submaximal spaces and compactifications
In this paper, we characterize spaces such that their one-point compactification (resp., Herrlich compactification) is weakly submaximal. We also...
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Strictly Zero-Dimensional Biframes and a Characterisation of Congruence Frames
Strictly zero-dimensional biframes were introduced by Banaschewski and Brümmer as a class of strongly zero-dimensional biframes including the...
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New Techniques for Computing Geometric Index
We introduce new general techniques for computing the geometric index of a link L in the interior of a solid torus T . These techniques simplify and...
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Weakly Motzkin Predecomposable Sets
We introduce and study the class of weakly Motzkin predecomposable sets, which are those sets in ℝ n that can be expressed as the Minkowski sum of a...
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Quasihomeomorphisms and meet-semilattice equivalences of generalized topological spaces
We study the properties of quasihomeomorphisms and meet-semilattice equivalences of generalized topological spaces. Since the results of lattice...
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Pressing Down Lemma for λ-trees and its applications
For any ordinal λ of uncountable cofinality, a λ -tree is a tree T of height λ such that | T α | < cf( λ ) for each α < λ , where T α = { x ∈ T : ht( x ) = α }....
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Skeletally Dugundji spaces
We introduce and investigate the class of skeletally Dugundji spaces as a skeletal analogue of Dugundji space. Our main result states that the...
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Near Sets: An Introduction
This article gives a brief overview of near sets. The proposed approach in introducing near sets is to consider a set theory-based form of nearness...
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Local Near Sets: Pattern Discovery in Proximity Spaces
The focus of this article is on various approaches to discerning patterns in nonempty sets endowed with a proximity (nearness) relation. Patterns...
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A Four for the Price of One Duality Principle for Distributive Spaces
In this paper we consider topological spaces as generalised orders and characterise those spaces which satisfy a (suitably defined) topological...
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Characterization of quasi-orbit spaces
Let G be a subgroup of the group Homeo( X ) of homeomorphisms of a topological space X . The class of an orbit O of G is the union of all orbits having...
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Rigid extensions of ℓ-groups of continuous functions
Let C ( X , ℤ), C ( X , ℂ) and C ( X ) denote the ℓ-groups of integer-valued, rational-valued and real-valued continuous functions on a topological space X ,...
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LJ-spaces
In this paper LJ -spaces are introduced and studied. They are a common generalization of Lindelöf spaces and J -spaces researched by E. Michael. A...
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Supercomplete topological spaces
Supercomplete topological spaces and other variants of supercompleteness are defined in this paper. The main idea is to give different...
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Division and k-th root theorems for Q-manifolds
We prove that a locally compact ANR-space X is a Q -manifold if and only if it has the Disjoint Disk Property (DDP), all points of X are homological Z ...
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Unique a-closure for some ℓ-groups of rational valued functions
Usually, an abelian ℓ-group, even an archimedean ℓ-group, has a relatively large infinity of distinct a -closures. Here, we find a reasonably large...
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Bounded tightness for weak topologies
In every Hausdorff locally convex space for which there exists a strictly finer topology than its weak topology but with the same bounded sets (like...