- #1
filter54321
- 39
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I'm having trouble understanding the definition of a Subspace/Induced/Relative Topology. The definitions I'm finding either don't define symbols well (at all).
If I understand correctly the definition is:
Given:
-topological space (A,[tex]\tau[/tex])
-[tex]\tau[/tex]={0,A,u1,u2,...un}
-subset B[tex]\subset[/tex]A
The subspace topology on B will be the intersection of B and every part of the topology of A
OR
[tex]\tau[/tex]B={0,B,B[tex]\bigcap[/tex]u1,B[tex]\bigcap[/tex]u2,...B[tex]\bigcap[/tex]un}
...I apologize in advance for my LATEX work.
If I understand correctly the definition is:
Given:
-topological space (A,[tex]\tau[/tex])
-[tex]\tau[/tex]={0,A,u1,u2,...un}
-subset B[tex]\subset[/tex]A
The subspace topology on B will be the intersection of B and every part of the topology of A
OR
[tex]\tau[/tex]B={0,B,B[tex]\bigcap[/tex]u1,B[tex]\bigcap[/tex]u2,...B[tex]\bigcap[/tex]un}
...I apologize in advance for my LATEX work.