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Question:1. Define dense set and an example of dense subset in usual topology. Show that
−   = − ° (1+1+4) 

Question:2.Consider the topology on = {, , , , } defined by = {∅, ,{},{, },{, , },{, , , }, {, , }} Determine the derived sets of  = {, , } and  = { }. (5) 

Question:3. What do you mean by neighborhood system? Show that a set  is open if and only if it is neighborhood of each of its elements. (2+5) 

Question:4. In a topological space
, , show that if  ⊆  then show that  ° ⊆ ° and ̅⊆ . (6) 

Question:5. What is the difference between a bases and a subbases? Let  be a base for the topological space
,  and  ∗ be a class of open sets containing . Show that  ∗ is also a base for
, . (2+4)

Instruction Files