Given a self-similar set E generated by a finite system Ψ of contracting similitudes of a complete metric space X we analyze a separation condition for Ψ , which is obtained if, in the open set condition, the open subset of X is replaced with an open set in the topology of E as a metric subspace of X. We prove that such a condition, which we call the restricted open set condition, is equivalent...

Often, when dealing with real-world recognition problems, we do not need, and often cannot have, knowledge of the entire set possible classes that might appear during operational testing. In such cases, need to think robust classification methods able deal "unknown" properly reject samples belonging never seen training. Notwithstanding, existing classifiers date were mostly developed for closed...

开放环境下的模式识别与文字识别应用中，新数据、新模式和新类别不断涌现，要求算法具备应对新类别模式的能力。针对这一问题，研究者们开始聚焦开放集文字识别（open-set text recognition，OSTR）任务。该任务要求，算法在测试（推断）阶段，既能识别训练集见过的文字类别，还能够识别、拒识或发现训练集未见过的新文字。开放集文字识别逐步成为文字识别领域的研究热点之一。本文首先对开放集模式识别技术进行简要总结，然后重点介绍开放集文字识别的研究背景、任务定义、基本概念、研究重点和技术难点。同时，针对开放集文字识别三大问题（未知样本发现、新类别识别和上下文信息偏差），从方法的模型结构、特点优势和应用场景的角度对相关工作进行了综述。最后，对开放集文字识别技术的发展趋势和研究方向进行了分析展望。;Text recognition is focused on transcription-...

In traditional semantic segmentation, knowing about all existing classes is essential to yield effective results with the majority of approaches. However, these methods trained in a Closed Set fail when new are found test phase, not being able recognize that an unseen class has been fed. This means they suitable for Open scenarios, which very common real-world computer vision and remote sensing...

 For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto  fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an o...

In this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.

in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.