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Semi-metrics, closure spaces and digital topology
1995
Theoretical Computer Science
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Within an appropriate category of these structures, ordinary spaces arise as inverse limits of digital spaces. ...
In the first instance, the structures can be taken to be (a slight generalization of) tech closure spaces. ...
The author is grateful to the referee for some corrections and improvements. ...
doi:10.1016/0304-3975(95)00053-y
fatcat:olklenlncbe7zbwl4tmyepn3sy
Semi-proximity continuous functions in digital images
1995
Pattern Recognition Letters
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Moreover, it is possible to describe all digital pictures used in computer vision and computer graphics as non-trivial semi-proximity spaces, which is not possible in classical topology. ...
Therefore, we use semi-proximity spaces to establish a formal relationship between the "topological" concepts of digital image processing and their continuous counterparts in [~" Especially interesting ...
It also follows from Theorem 1.2 that every topological space is a semi-proximity space, since every topological space is a Cech closure space. ...
doi:10.1016/0167-8655(95)00069-s
fatcat:c6flng3aizbrhcawxavr7ugztu
Rough semi-uniform spaces and its image proximities
2020
Electronic Research Archive
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In this paper, we introduce the concept of rough semi-uniform spaces as a supercategory of rough pseudometric spaces and approximation spaces. ...
Applications of rough semi-uniform spaces in the construction of proximities of digital images is also discussed. 2020 Mathematics Subject Classification. ...
The category of rough semi-uniform spaces is shown to be a supercategory of the categories of metric spaces, ultrametric spaces and rough metric spaces with their respective mappings. ...
doi:10.3934/era.2020060
fatcat:ngqm7vumkzaplmtppzp3pdmhha
Symposium lectures
1992
Topology and its Applications
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Descriptive
sets and the topology of non-separable
Banach spaces
Countably
compact topological
groups
Groups, semi-groups
and generalized
metric spaces
Spaces X such that C(X)/P
is a valuation ...
locales
Partitions of topological
spaces
K-spaces and spaces with a v-hereditarily
closure-
preserving
k-network
The dynamics of indecomposable
continua
A -sets
On dimension
theory
A topological ...
doi:10.1016/0166-8641(92)90072-8
fatcat:4wxhfqv5dfcqddpsq3lz4awhna
A note on \alpha-semi countability and related topics
2007
International Mathematical Forum
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In this paper are introduced the concepts of α-semi base for a topological space (X, Ω) and a monotone operation α : P(X) → P(X) associated to the topology Ω, with the purpose of generalizing the countability ...
Furthermore, imposing certain condition on the operation α we obtain a simple expression for semi opens sets in terms of nowhere dense sets, and we establish an analogue version of Baire-Kuratowski theorem ...
Khalimsky-is the basic building block of the digital n-space which is the topological model of the computer and the television screen for n = 2 and the digitized image of a movie when the time is discretized ...
doi:10.12988/imf.2007.07237
fatcat:ignm2rc6ljh57ehduqqizyxqly
Applications of Near Sets
2012
Notices of the American Mathematical Society
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Resemblance is determined by considering set descriptions defined by feature vectors (n-dimensional vectors of numerical features that represent characteristics of objects such as digital image pixels) ...
based on human perception [44, 76, 49, 51, 56] that arise in areas such as image analysis [52, 14, 41, 48, 17, 18], image processing [41], face recognition [13], ethology [63], as well as engineering and ...
This result was used by Domiaty and Laback in a study of semi-metric spaces in general relativity [7] . This puts S. ...
doi:10.1090/noti817
fatcat:o7cltpuktzhdrhaod7gjchpvoi
Nearness in Digital Images and Proximity Spaces
[chapter]
2000
Lecture Notes in Computer Science
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After this we characterize proximally continuous mappings in metric spaces. ...
Finally, we show by example that the "proximite complexity" of a finite covering in a digital picture may be too high to be adequately depicted in a finite topological space. ...
Then (X,¯) is a closure (resp. topological) space (the closure¯is said to be induced by the proximity π). ...
doi:10.1007/3-540-44438-6_7
fatcat:nt5rlodblrhqzlptpeaztdwqnq
Page 581 of Mathematical Reviews Vol. , Issue 97A
[page]
1997
Mathematical Reviews
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B. (4-LNDIC-C; London) Semi-metrics, closure spaces and digital topology. Topology and completion in semantics (Chartres, 1993). Theoret. Comput. Sci. 151 (1995), no. 1, 257-276. ...
Within an appropriate category of these structures, ordinary spaces arise as inverse limits of digital spaces. ...
Idealization of some weak separation axioms
[article]
1998
arXiv
pre-print
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We concentrate our attention on the separation axioms between T_0 and T_2. We prove that if (X,τ, I) is a semi-Alexandroff T_ I-space and I is a τ-boundary, then I is completely codense. ...
An ideal is a nonempty collection of subsets closed under heredity and finite additivity. The aim of this paper is to unify some weak separation properties via topological ideals. ...
In Digital Topology [12] several spaces that fail to be T 1 are important in the study of the geometric and topological properties of digital images [12, 14] . ...
arXiv:math/9810075v1
fatcat:gxbtypajeje6rdt6hfw3q6w5ji
Semi-metric networks for recommender systems
[article]
2012
arXiv
pre-print
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We use this semi-metric behavior to issue recommendations, and discuss its relationship to transitive closure on fuzzy graphs. ...
Weighted graphs obtained from co-occurrence in user-item relations lead to non-metric topologies. ...
We use this semi-metric behavior to issue recommendations, and discuss its relationship to transitive closure on fuzzy graphs. ...
arXiv:1209.1719v1
fatcat:w66chl2xxbgfvcowpv3jqmcvny
The distance backbone of complex networks
2021
Journal of Complex Networks
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paths and those that do not but are involved in other network phenomena. ...
This is important for understanding the dynamics of spread and communication phenomena in real-world networks. ...
Acknowledgements The authors thank Olaf Sporns and Giovanni Ciampaglia for sharing data used in the analysis and for many useful conversations to understand the results. ...
doi:10.1093/comnet/cnab021
fatcat:dqsextlrnne7pggipmnunx3oa4
Page 4967 of Mathematical Reviews Vol. , Issue 2000g
[page]
2000
Mathematical Reviews
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Summary: “It is shown that semi-regularity is hereditary in a para-S-closed space, and in a para-S-closed space all the sets constructed from a semi-regular set by the closure, interior and complementation ...
a formal notion of approximation to (topological) digital topology. ...
The Fuzzification of Classical Structures: A General View
2015
International Journal of Computers Communications & Control
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, fuzzy topological spaces, fuzzy metric spaces, fuzzy topological vector spaces, fuzzy normed linear spaces. ...
The aim of this survey article, dedicated to the 50th anniversary of Zadeh's pioneering paper "Fuzzy Sets" (1965), is to offer a unitary view to some important spaces in fuzzy mathematics: fuzzy real line ...
[33] The closure and the interior of a fuzzy set µ in a fuzzy topological space (X, T ) are defined by µ = inf{µ 1 : µ ⊆ µ 1 and C(µ 1 ) ∈ T } • µ = sup{µ 1 : µ 1 ⊆ µ and µ 1 ∈ T } . ...
doi:10.15837/ijccc.2015.6.2069
fatcat:7som5tg4vzayhn3eiddzaqu6z4
Semi-metric Networks for Recommender Systems
2012
2012 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology
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We use this semi-metric behavior to issue recommendations, and discuss its relationship to transitive closure on fuzzy graphs. ...
Weighted graphs obtained from co-occurrence in user-item relations lead to non-metric topologies. ...
A special case of distance closure is the metric closure, where f (x, y) = min(x, y) and g(x, y) = x + y. ...
doi:10.1109/wi-iat.2012.245
dblp:conf/iat/SimasR12
fatcat:wuncn745xjgebog3roexgtifha
On non-Hausdorff spaces
1992
Topology and its Applications
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., On non-Hausdorff spaces, Topology and its Applications 44 (1992) 331-340. This paper surveys some recent work on topological spaces which need not satisfy the Hausdorff separation property. ...
It advocates change (of the definition, of the problem, of the topology) as a useful topological tool. ...
To illustrate, we consider the semi-regularization topology TTY of a topological space (X, 9) . ...
doi:10.1016/0166-8641(92)90106-a
fatcat:cipyphcd5vdoveejyg2ajbgome
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