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- I need help in order to prove a result stated by Willard linking the notions of interior and closure in a topological space ...

I am reading Stephen Willard: General Topology ... ... and am currently focused on Chapter 2: Topological Spaces and am currently focused on Section 3: Fundamental Concepts ... ...

I need help in order to fully understand a result or formula given by Willard concerning a link between closure and interior in a topological space ... ..The relevant text reads as follows:

In the above text by Willard we read the following:

" ... ... The strictly formal nature of this duality can be brought out in observing that

##X - E^{ \circ } = \overline{ X - E }## ... ... "Can someone please demonstrate (formally and rigorously) that ... given the definitions and results regarding closure and interior used by Willard ... ##X - E^{ \circ } = \overline{ X - E }## ... ...The definitions and results regarding closure used by Willard are as follows:

Help will be much appreciated ... ...

Peter

I need help in order to fully understand a result or formula given by Willard concerning a link between closure and interior in a topological space ... ..The relevant text reads as follows:

In the above text by Willard we read the following:

" ... ... The strictly formal nature of this duality can be brought out in observing that

##X - E^{ \circ } = \overline{ X - E }## ... ... "Can someone please demonstrate (formally and rigorously) that ... given the definitions and results regarding closure and interior used by Willard ... ##X - E^{ \circ } = \overline{ X - E }## ... ...The definitions and results regarding closure used by Willard are as follows:

Help will be much appreciated ... ...

Peter