induced topology sentence in Hindi
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- And the induced topology agrees with the product topology.
- Proximity maps will be continuous between the induced topologies.
- The metric identification preserves the induced topologies.
- The induced topology is the indiscrete topology.
- The induced topology is the original topology.
- The Helly space has a topology; namely the induced topology as a subset of " I I ".
- Now it is obvious that if a system is weaker than another, the induced topology is weaker . . but what about the converse?
- One can show that the compact subsets of " X " c and " X " coincide and the induced topologies are the same.
- Because any " G " ? subset of a Polish space is again a Polish space, the theorem also shows that any " G " ? subset of a Polish space is the union of a countable set and a set that is perfect with respect to the induced topology.
- In general the group \ Gamma \ cap \ overline H is equal to the congruence closure of H in \ Gamma, and the congruence topology on \ Gamma is the induced topology as a subgroup of \ mathbf G ( \ mathbb A _ f ), in particular the congruence completion \ overline \ Gamma is its closure in that group.
- The limit of a sequence of points \ left ( x _ n : n \ in \ mathbb { N } \ right ) \; in a topological space " T " is a special case of the limit of a function : the domain is \ mathbb { N } in the space \ mathbb { N } \ cup \ lbrace + \ infty \ rbrace with the induced topology of the affinely extended real number system, the range is " T ", and the function argument " n " tends to + ", which in this space is a limit point of \ mathbb { N }.
- I'm happy with the equivalence of convergence under the given metric iff we get convergence for all the seminorms; so I guess my final question is about the correspondence between the limits and the topology : if we know ( as in this case ) that convergence in the induced topology from the seminorms is the same as convergence in a different topology ( such as the product topology here ), why does that necessarily mean the 2 topologies themselves are the same ? ( How do we know there isn't some weird collection of open sets, not the same as the product topology, which gives us convergence in the seminorms iff we have convergence in the product topology?
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