Point-set topology grew out ofCantor's studies of sets of real numbers. As such, its central aim is to provide an appropriate context for generalizing such properties of the real numbers as theBolzano- Weierstrassproperty(波尔查诺-维尔斯特拉斯性质,也叫聚点定理)and theHeine-Borel property(海涅...
I shall now explain a bit of the intuition behind the proof of Tychonoff's theorem using the Alexander subbase theorem. I believe it should be more or less immediately for anyone who has studied boolean algebra deeply. A difficulty some students might have with point set topology is the exis...
当涉及Tychonoff定理时，我们需要处理乘积空间。因此，我们进一步定义：定义2：设[公式]和[公式]是拓扑空间，如果序列[公式]在[公式]中收敛到某个[公式]，则[公式]在[公式]中的序列[公式]也收敛到[公式]。换句话说，如果[公式]在[公式]中是开集，那么[公式]在[公式]中也是开集。定义3：对于任意...
Sourav Chakraborty1. C/o Suprakash Chakraborty, D-138, Grissom Street, Bidhan Nagar Durgapur 713 212 W.B., India ;Springer IndiaResonanceSourav Chakraborty, Point Set Topological Proof of "no-retraction" Theorem for 2 and 3 dimensional cases. www.cs.uchicago.edu/∼sourav/papers/topology.pdf...
Notes on Introductory Point-Set Topology 来自 Semantic Scholar 喜欢 0 阅读量: 34 作者: A Hatcher 摘要: In this note we prove the following result due to Milnor ((5), Theorem 4·1).(Received June 01 1966) 被引量: 1 年份: 2014 ...
Of nate, much room remains in bridging computational discrete geometry or topology with the theoretical point set topology. In addition to 3D visualization purposes, over the past few years a few teams have explored other aspects of mesh manipulation. Related to the α-shape structures (Edels...
In the next part of the article we will discuss some other contractive type conditions. Let (X,d) be a complete metric space andTbe a selfmapping ofX.\({\mathbb {R}}_+\)denotes the set of all non-negative reals. The Banach theorem can be formulated in the form: every Banach contra...
Bellman OperatorUniform ConvergenceThis study introduces a new definition of a metric that corresponds with the topology of uniform convergence on any compact set, and shows both the existence of a unique fixed point of some operator by using this metric and that the iteration of such an operator...
Generalized saddle points theorems for set-valued mappings in locally generalized convex spaces In the paper, the notions of generalized loose (weak) saddle points for set-valued mappings are introduced. By applying the fixed point theorem and the sca... QB Zhang,MJ Liu,CZ Cheng - 《Nonlinear...
Define weak point. weak point synonyms, weak point pronunciation, weak point translation, English dictionary definition of weak point. Noun 1. weak point - an attribute that is inadequate or deficient liability - the quality of being something that holds