4 Answered Questions for the topic Topology

12/27/19

#### Why are there two definitions of "open"?

I am learning topology, and I don't understand about an open set.So I learned a definition of open set.A subset U of M is called open (with respect to d) if for every x ∈ U there exists a real...
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05/25/19

#### An infinite limit exists or doesn't exist?

I have several months dealing with the situation of the existence of a limit. The way I teach to my students is the limit at a exists if the two-sided limits exist and are the same.Most calculus...
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02/11/18

#### Show that the set GL(n, R) of invertible n × n real matrices is open in the space of n × n matrices (metric spaces, Real analysis)

Show that the set GL(n, R) of invertible n × n real matrices is open in the space of n × n matrices, with the metric being the Euclidean metric in Rn^2 when a matrix is identiﬁed with a long, n2...
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01/08/18

#### Let X: [0,1] being in all real numbers be given by X(x) = max{x-0.5,0}. Find the inverse images of all intervals [a,b]

Let X: [0,1] being in all real numbers be given by X(x) = max{x-0.5,0}. Find the inverse images of all intervals [a,b] Due to lack of examples related to the theory, I am unable to properly write...
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