Why is the indiscreet topology important
Set theoretical topology
Algebraic Topology pp 9-65 | Cite as
In metric spaces, the spatial relationship of points is described by their distance from one another. With the help of the metric, the concept of environment is introduced and open and closed sets are defined. These open sets have the following characteristic properties: The union of any number of open sets is open, and the intersection of finitely many open sets is also open. These two properties turned out to be fundamental for an axiomatic description of spatial relationships. Becomes from alien subsets of a set X denotes a system of subsets which is closed with respect to the formation of finite averages and arbitrary unions, and in addition X itself and contains the empty set, this can be broken down as a system of open sets X consider. Such a system is called topology X, and some of the definitions and theorems in connection with open sets, which are known from the introductory courses on calculus, can be applied to the set Xon which a topology is marked. So can each point of X assign a system of environments, and with the help of the concept of environment, the concepts of open core, closed shell and edge of a subset can be transferred directly to the abstract set with a topology. The same applies to the concept of continuous mapping.
Unable to display preview. Download preview PDF.
Authors and Affiliations
- 1. Department of Mathematics, University of Dortmund, Dortmund 50, Germany
- Will Amazon Prime Video Destroy Netflix
- Which Marvel character would you totally smash?
- Who runs the secretariat
- What kind of person was Joey Ramone
- Why can't anyone challenge Roger Federer
- What did you do to cheat students
- Who designed the Headspace app
- Which scientist explained Einstein's photoelectric equation
- What are the benefits of garlic milk
- What's your rating of Shoegaze
- Can drive a car seat in front
- What were the main events of the First World War
- What is an ordinary differential equation
- What is a biometric input
- How long are dog periods
- What is OBE software
- What if a hacker uses a keylogger
- How many electrons does chlorine contain?
- What is the role of DMSO in PCR
- When will Indians be liberated from India?
- How to Monitor the Progress in Search Engine Optimization
- Very hot chillies harm your health
- Wish lists are a viable online business
- Which gums contain xylitol?
- What language is spoken in Cardiff
- What crimes did Bernie Madoff commit
- How are eyebrows plucked with string?
- How old is my house
- Hosting of porn sites
- What is actually giving you a headache
- Is the gigabyte motherboard best
- What is the Dupler Effect