The language of pre-topology in knowledge spaces
We systematically study some basic properties of the theory of pre-topological spaces, such as, pre-base, subspace, axioms of separation, connectedness, etc. Pre-topology is also known as knowledge space in the theory of knowledge structures. We discuss the language of axioms of separation of pre-topology in the theory of knowledge spaces, the relation of Alexandroff spaces and quasi ordinal spaces, and the applications of the density of pre-topological spaces in primary items for knowledge spaces. In particular, we give a characterization of a skill multimap such that the delineate knowledge structure is a knowledge space, which gives an answer to a problem in \cite{falmagne2011learning} or \cite{XGLJ} whenever each item with finitely many competencies; moreover, we give an algorithm to find the set of atom primary items for any finite knowledge spaces.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
GIST: Multimodal Knowledge Extraction and Spatial Grounding via Intelligent Semantic Topology
Navigating complex, densely packed environments like retail stores, warehouses, and hospitals poses a significant spatial grounding challenge for humans and embodied AI. In these spaces, dense visual features quickly bec…
FedTopo: Relation-Level Topology Sharing for Model-Heterogeneous Federated Learning
Federated learning (FL) enables collaborative learning over decentralized data silos without centralizing raw data. However, heterogeneous local architectures often induce non-aligned representation spaces, making it dif…
Federated LearningMasFACT: Continual Multi-Agent Topology Learning via Geometry-Aware Posterior Transfer
Multi-agent systems (MAS) powered by large language models (LLMs) have emerged as a powerful paradigm for complex problem solving, where performance critically depends on the underlying inter-agent communication topology…
Kernel Mean Embedding Topology: Weak and Strong Forms for Stochastic Kernels and Implications for Model Learning
We introduce a novel topology, called Kernel Mean Embedding Topology, for stochastic kernels, in a weak and strong form. This topology, defined on the spaces of Bochner integrable functions from a signal space to a space…
Multi-Granularity Class Prototype Topology Distillation for Class-Incremental Source-Free Unsupervised Domain Adaptation
This paper explores the Class-Incremental Source-Free Unsupervised Domain Adaptation (CI-SFUDA) problem, where the unlabeled target data come incrementally without access to labeled source instances. This problem poses t…
class-incremental learningDomain AdaptationRepresentation LearningSource-Free Domain Adaptation+1