Revisit open and closed domains

[daanhb]

In the package IntervalSets, isopen and isclosed will soon be renamed to isopenset and isclosedset (see https://github.com/JuliaMath/IntervalSets.jl/issues/59). We will have to follow suit.

One issue I noticed is that the current definition of the boundary of an interval is unexpected. It does not include endpoints if the interval is open:

julia> boundary(ClosedInterval(0.,1.))
a union of 2 domains:
    1.  : Point{Float64}(0.0)
    2.  : Point{Float64}(1.0)

julia> boundary(OpenInterval(0.,1.))
the empty space with eltype Float64

If an interval is seen as a subset of the real line, then its boundary includes both endpoints, regardless of whether the interval is open or not. I.e., I would expect:

boundary(d::AbstractInterval) = Point(leftendpoint(d)) ∪ Point(rightendpoint(d))

Then, one could define the closure of an open interval as the corresponding closed interval, and the interior of the closed interval as the open one - the boundary would be the difference between the two.

Is there a reason for the current implementation? Now seems like a good time to change it.

[daanhb]

I have tentatively applied that change in #55. It seems to break ApproxFun, which was to be expected. The rename to isopenset and isclosedset is yet to happen.

[daanhb]

@JuliaRegistrator register()

[JuliaRegistrator]

Registration pull request created: JuliaRegistries/General/13423

After the above pull request is merged, it is recommended that a tag is created on this repository for the registered package version.

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git tag -a v0.3.0 -m "<description of version>" f1a2bbb3c041ade4d82e4777fbaf0f2c42dd56e7
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