Should I use "Map" or "Select" for new functor-like operators in C#?

Question

I'm designing a type in C# that will be used as an algebraic type in a functional style, but is not a collection type and does not implement IEnumerable. If this type is a Functor, should I name its projection method Select or Map? Similarly, if it's Filterable, should I name that method Filter or Where? What are the pros and cons of following LINQ's naming convention vs. matching the larger functional community?

For concrete examples, consider things like Optional<T> and IObservable<T>.

Considerations:

• If we choose Select over Map, what happens when the type also fits other common algebraic structures like Contravariant? Do we keep Contramap and accept the mismatch with Select? Do we make up names like ContraSelect?
• If we choose Map over Select, how "collection-like" can our type get before we're more or less in direct conflict with LINQ?
• Following LINQ names allows for query syntax support, but do we want to encourage or discourage query syntax for types that are very unlike IQueryable?