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Trans-separability in spaces of continuous vector-valued functions

100%

Khan L. A.

Demonstratio Mathematica

2004

tom Vol. 37, nr 3

611--617

Let X be a completely regular Hausdorff space and E a Hausdorff topological vector space (TVS). In this note, we study the notion of trans-separability for certain subspaces of Cb(X,E) endowed with the cr-compact-open and some related topologies.

Treasure Trove at Banacha. Set Patterns in Descriptive Proximity Spaces

75%

Peters J. F. , Ramanna S.

Fundamenta Informaticae

2013

tom Vol. 127, nr 1-4

357--367

This paper introduces descriptive set patterns that originated from our visits with Zdzisław Pawlak and Andrzej Skowron at Banacha and environs in Warsaw. This paper also celebrates the generosity and caring manner of Andrzej Skowron, who made our visits to Warsaw memorable events. The inspiration for the recent discovery of descriptive set patterns can be traced back to our meetings at Banacha. Descriptive set patterns are collections of near sets that arise rather naturally in the context of an extension of Solomon Leader's uniform topology, which serves as a base topology for compact Hausdorff spaces that are proximity spaces. The particular form of proximity space (called EF-proximity) reported here is an extension of the proximity space introduced by V. Efremovič during the first half of the 1930s. Proximally continuous functions introduced by Yu.V. Smirnov in 1952 lead to pattern generation of comparable set patterns. Set patterns themselves were first considered by T. Pavlidis in 1968 and led to U. Grenander's introduction of pattern generators during the 1990s. This article considers descriptive set patterns in EF-proximity spaces and their application in digital image classification. Images belong to the same class, provided each image in the class contains set patterns that resemble each other. Image classification then reduces to determining if a set pattern in a test image is near a set pattern in a query image.