On certain versions of straightness
| Autor: | Pratulananda Das, Sudip Kumar Pal, Nayan Adhikary |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Property (philosophy) Continuous function Closed set 010102 general mathematics Cauchy distribution Computer Science::Computational Geometry 01 natural sciences 010101 applied mathematics Metric space Uniform continuity Cover (topology) Geometry and Topology 0101 mathematics Mathematics |
| Zdroj: | Topology and its Applications. 284:107369 |
| ISSN: | 0166-8641 |
| Popis: | Straight spaces are metric spaces X having the property that for a cover X = A ∪ B by two closed sets, any continuous function f : X → R is uniformly continuous provided it is so on each of the sets A and B (it is actually called ‘2-straight’ but is easier to deal with [8] ). In this paper we consider this nice idea and instead of uniformly continuous functions, we consider Cauchy regular functions [18] and ward continuous functions [12] , as these classes of functions strictly lie between the classes of continuous and uniformly continuous functions. In the process we obtain two natural variations of straightness which we name pre-straight and W-straight spaces respectively. We primarily investigate these notions along with another notion called pre ( ⁎ ) -straight which actually helps us to obtain a better understanding of the relation-ship between the notions of straight and pre-straight ness. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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