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To start studying topology, what basic knowledge should I have?
Another said:To start studying topology, what basic knowledge should I have?
Completely true and I basically agree with what you said. But there is a dark side of this moon. The example of metric spaces in mind, usually a Euclidean plane or sometimes a volume, can also be a burden learning topology, simply because metric spaces tend to be the "nice" topologies and there are a lot more which do not have those properties. I found it always a bit challenging to imagine spaces which e.g. aren't Hausdorff. So as basic as metric spaces are, and yes, they are indeed the origin of general topology, as obstructive they can be.Math_QED said:For the rest there are not really prequisites, but I highly recommend to learn about metric space analysis first, which introduces concepts like open sets and closed sets etc.
What topology are you interested in and what is your level?Another said:To start studying topology, what basic knowledge should I have?
now i am study in Bachelor of Science (Physics)lavinia said:What topology are you interested in and what is your level?
I just want to have some knowledge about topologyAnother said:now i am study in Bachelor of Science (Physics)
I want to apply knowledge about topology to physics problem
Can you give an example?Another said:now i am study in Bachelor of Science (Physics)
I want to apply knowledge about topology to physics problem
Yes, but this is the question. Basics are found in any "Introduction to Topology" book and will mainly deal with the set theoretic part of it. If you mention physics, then manifolds and their topologies come to mind, which is a very different approach, but very likely presumes the set theoretic basics as given. If you say physics, but mean cosmology, then algebraic topology might be important, which is again another approach. Compared to its age, topology well-nigh exploded into various branches which are each by themselves more or less sophisticated. As a starting point, any book with "Introduction" in the title will probably be a good choice, as these subjects (separation axioms, limit points, compactness etc.) are of general interest and basic to many other realms of topology as well as analysis.Another said:I just want to have some knowledge about topology
lavinia said:Can you give an example?
Another said:I need knowledge of topology before studying relativity theory.
George Jones said:Why?
Math_QED said:Maybe because general relativity uses topology?
(**) A cute little example uses the open cover definition of compactness to show that all compact spacetimes contained time loops.George Jones said:As a quantum mechanics book suitable for someone with your background, I highly recommend "Quantum Theory for Mathematicians" by Hall,
https://www.amazon.com/dp/146147115X/?tag=pfamazon01-20
It is a very beautiful book.
Another said:I do not have an example.
but I have an interest in Relativity theory.
I need knowledge of topology before studying relativity theory.
Topology is a branch of mathematics that studies the properties and structures of spaces that are preserved under continuous deformations. This means that objects in topology can be stretched, twisted, and bent without changing their essential characteristics.
Topology has many applications in various fields, including physics, computer science, biology, and engineering. It is used to study the shape of molecules, analyze networks and data, understand the behavior of fluids, and solve optimization problems, among others.
The main concepts in topology include continuity, connectedness, compactness, and convergence. Continuity refers to the smoothness and lack of breaks in a function or space. Connectedness refers to the ability to travel from one point to another without leaving the space. Compactness refers to the property of a space to have no holes or gaps. Convergence refers to the idea of approaching a limit or a fixed point.
While geometry studies the properties of objects in a fixed space, topology focuses on the properties of spaces themselves. In topology, the shape or size of an object is not important, only its connectivity and continuity. This allows for more abstract and generalized concepts compared to the specific measurements and angles studied in geometry.
Some recommended resources for studying topology include textbooks such as "Topology" by James R. Munkres and "Introduction to Topology" by Bert Mendelson. Online resources such as the Topology Atlas and the Topology Zoo also offer a wide range of information and examples. Additionally, attending seminars and workshops, or joining a topology study group can provide valuable opportunities for learning and discussion.