Strongly proximal continuity &amp; strong connectedness

Peters, James F.; Guadagni, C.

doi:10.1016/j.topol.2016.02.008

Cited by 7 publications

(5 citation statements)

References 15 publications

(10 reference statements)

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“…Once we have geometrical primitive of nearness, the formal level of our approach is compatible with tolerance and nearness models ( (Peters, 2007), (Peters andWasilewski, 2009, 2012); for an analysis of proximity cp. also (Peters and Guadagni, 2016)).…”

Section: Discussionmentioning

confidence: 87%

Topologic and Geometric Structure of Spatial Relations in Latvian: an Experimental Analysis of RCC

Šķilters¹,

Zariņa²,

Žilinskaitė-Šinkūnienė³

et al. 2020

BJMC

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In this study we experimentally test topological and geometric relations as encoded in Latvian. The task of the subject is to describe different combinations of two geometric objects presented in a randomized order. For the in-group experiment two circlesdark and light-were used according to the topological principles of Region Connection Calculus further extended with simple relational variables representing proximity, orientation, object size, and partial occlusion. The results show that both topological and geometric features determine the number of words used in the description of the respective relations and accuracy of the description. Further, we explored the most common words used for the description of general spatial relations and tested the differences associated with the experimental variables. It was concluded that topological and geometric relations matter in the linguistic representation of space but to a differing degree. Our results also indicate that spatial relations at the linguistic level are represented categorically and rarely encode fine-grained information.

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Section: Discussionmentioning

confidence: 87%

Topologic and Geometric Structure of Spatial Relations in Latvian: an Experimental Analysis of RCC

Šķilters¹,

Zariņa²,

Žilinskaitė-Šinkūnienė³

et al. 2020

BJMC

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“…This article carries forward recent work on strong proximities [34,35,37,39] and their applications [19,31], which is a direct result of work on proximity [1,3,7,8,9,12,23,26,27,28,29,33]. Applications of the results in this paper are given in terms of the atlases and charts of proximal manifolds and what are known as…”

Section: Introductionmentioning

confidence: 88%

Strong Proximities on Smooth Manifolds and Vorono\" i Diagrams

Peters¹,

Guadagni²

2015

Preprint

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This article introduces strongly near smooth manifolds. The main results are (i) second countability of the strongly hit and far-miss topology on a family B of subsets on the Lodato proximity space of regular open sets to which singletons are added, (ii) manifold strong proximity, (iii) strong proximity of charts in manifold atlases implies that the charts have nonempty intersection. The application of these results is given in terms of the nearness of atlases and charts of proximal manifolds and what are known as Voronoï manifolds.

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“…In the discussion that follows we attempt to formulate the notion of a path in terms of hyperconnectedness. Similar to proximity [8] these relations can be used to define continuity.…”

Section: Hyperconnected Genralization Of Pathmentioning

confidence: 99%

Hyperconnected Relator Spaces. CW Complexes and Continuous Function Paths that are Hyperconnected

Ahmad,

Peters

2018

Preprint

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This article introduces proximal cell complexes in a hyperconnected space. Hyperconnectedness encodes how collections of path-connected sub-complexes in a Alexandroff-Hopf-Whitehead CW space are near to or far from each other. Several main results are given, namely, a hyper-connectedness form of CW (Closure Finite Weak topology) complex, the existence of continuous functions that are paths in hyperconnected relator spaces and hyperconnected chains with overlapping interiors that are path graphs in a relator space. An application of these results is given in terms of the definition of cycles using the centroids of triangles.

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Strongly proximal continuity & strong connectedness

Cited by 7 publications

References 15 publications

Topologic and Geometric Structure of Spatial Relations in Latvian: an Experimental Analysis of RCC

Topologic and Geometric Structure of Spatial Relations in Latvian: an Experimental Analysis of RCC

Strong Proximities on Smooth Manifolds and Vorono\" i Diagrams

Hyperconnected Relator Spaces. CW Complexes and Continuous Function Paths that are Hyperconnected

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