Author: Timothy Nugent TaylorPublisher:
ISBN:
Category :
Languages : en
Pages : 26
Book Description
Separation Axioms for Abstract Topological Spaces
Author: Timothy Nugent TaylorPublisher:
ISBN:
Category :
Languages : en
Pages : 26
Book Description
Separation Axioms, Covering Properties and Inverse Limits Generated by Developable Topological Spaces
Author: Harald BrandenburgPublisher:
ISBN:
Category : Set theory
Languages : en
Pages : 100
Book Description
Separation in Point-Free Topology
Author: Jorge PicadoPublisher: Springer Nature
ISBN: 3030534790
Category : Mathematics
Languages : en
Pages : 296
Book Description
This book is the first systematic treatment of this area so far scattered in a vast number of articles. As in classical topology, concrete problems require restricting the (generalized point-free) spaces by various conditions playing the roles of classical separation axioms. These are typically formulated in the language of points; but in the point-free context one has either suitable translations, parallels, or satisfactory replacements. The interrelations of separation type conditions, their merits, advantages and disadvantages, and consequences are discussed. Highlights of the book include a treatment of the merits and consequences of subfitness, various approaches to the Hausdorff's axiom, and normality type axioms. Global treatment of the separation conditions put them in a new perspective, and, a.o., gave some of them unexpected importance. The text contains a lot of quite recent results; the reader will see the directions the area is taking, and may find inspiration for her/his further work. The book will be of use for researchers already active in the area, but also for those interested in this growing field (sometimes even penetrating into some parts of theoretical computer science), for graduate and PhD students, and others. For the reader's convenience, the text is supplemented with an Appendix containing necessary background on posets, frames and locales.
Separation axioms of topological spaces
Author: Roy Dean AlstonPublisher:
ISBN:
Category : Topology
Languages : en
Pages : 74
Book Description
Separation Axioms on Bipolar Hypersoft Topological Spaces
Author: Sagvan Y. MusaPublisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 16
Book Description
According to its definition, a topological space could be a highly unexpected object. There are spaces (indiscrete space) which have only two open sets: the empty set and the entire space. In a discrete space, on the other hand, each set is open. These two artificial extremes are very rarely seen in actual practice. Most spaces in geometry and analysis fall somewhere between these two types of spaces. Accordingly, the separation axioms allow us to say with confidence whether a topological space contains a sufficient number of open sets to meet our needs. To this end, we use bipolar hypersoft (BHS) sets (one of the efficient tools to deal with ambiguity and vagueness) to define a new kind of separation axioms called BHS e Ti-space (i = 0, 1, 2, 3, 4).
Separation Axioms in Topological Spaces
Author: Robert Kenneth SmartPublisher:
ISBN:
Category : Axions
Languages : en
Pages : 162
Book Description
Topology
Author: Marco ManettiPublisher: Springer
ISBN: 3319169580
Category : Mathematics
Languages : en
Pages : 315
Book Description
This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.
Separation Axioms of Topological Spaces
Author: Robert M. FoxA New Separation Axiom for Topological Spaces
Author: Phillip Alan HartmanPublisher:
ISBN:
Category : Topology
Languages : en
Pages : 24
Book Description
Counterexamples for the Separation Axioms of Topological Spaces
Author: Roland Francis StreitPublisher:
ISBN:
Category : Topology
Languages : en
Pages : 6
Book Description