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Semi-metrics, closure spaces and digital topology

M.B. Smyth
1995 Theoretical Computer Science  
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

Longin Latecki, Frank Prokop
1995 Pattern Recognition Letters  
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

Surabhi Tiwari, ,Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj-211004, India, Pankaj Kumar Singh
2020 Electronic Research Archive  
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  
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

Y. Quintana
2007 International Mathematical Forum  
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

Jim Peters, Som Naimpally
2012 Notices of the American Mathematical Society  
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]

Pavel Pták, Walter G. Kropatsch
2000 Lecture Notes in Computer Science  
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  
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]

Francisco G. Arenas, Julian Dontchev, Maria Luz Puertas
1998 arXiv   pre-print
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]

Tiago Simas, Luis M. Rocha
2012 arXiv   pre-print
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

Tiago Simas, Rion Brattig Correia, Luis M Rocha, Ernesto Estrada
2021 Journal of Complex Networks  
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  
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

Ioan Dzitac
2015 International Journal of Computers Communications & Control  
, 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

Tiago Simas, Luis M. Rocha
2012 2012 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology  
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

Ivan L. Reilly
1992 Topology and its Applications  
., 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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