

Venn diagrams
Topology of sets
We are generalizing the notion of container and interval in terms of boundaries.
If possible, we want to ground all analytic structure in the topology of the Closed Loop, mapping from serial/linear sequential forms into the holistic allatonce everythingatthesametime framework of the loop.
So a question arises.
How can we define the contents of a Venn diagram with its continuous circlebased boundary, so as to distinguish "what is IN the set" (inside the circle) and "what is NOT IN the set" (outside the circle)?
The answer is  this structure is hierarchical.
Is the hierarchical model isomorphic to the Venn diagram? We are studying the meaning of isomorphic  along with other related concepts that might be grounded together as a "family"  such as identity, equality, similarity.

Set, venn diagram, dimensionality, boundary
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Set, venn diagram, dimensionality, boundary
Define the concept of set in terms of boundary and its objects in terms of dimensionality
(abstract object, concrete object)
At a minimum, a set has a boundary  things IN the set, and things NOT IN the set
Can that be specified by dimensionality?
Yes, as long as the objects are defined in terms of dimensionality
Abstract objects are defined in terms of dimensionality, and then a mapping/correlation is established by the abstract object (the word, the symbol) and the concrete object ("the actual thing" it is pointing to))

What is a container?
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We want to generalize the notion of container based on boundaries, and following the ideal and intuitive definitions of Venn diagrams.
Are Venn diagrams hierarchical in every case?
 Containers
 HTML tables  rows [tr] "table row" and columns [td] intersect to form cells, which contain something  td  "table data"?
 Boundaries
 Circles
 Boxes
 Matrix (matrices)
 Row / column intersection = cell
Reference
In computer science, a container is a class, a data structure, or an abstract data type (ADT) whose instances are collections of other objects.
In other words, they store objects in an organized way that follows specific access rules. The size of the container depends on the number of objects (elements) it contains. Underlying (inherited) implementations of various container types may vary in size and complexity, and provide flexibility in choosing the right implementation for any given scenario.
Function and properties
Containers can be characterized by the following three properties:
 access, that is the way of accessing the objects of the container. In the case of arrays, access is done with the array index. In the case of stacks, access is done according to the LIFO (last in, first out) order and in the case of queues it is done according to the FIFO (first in, first out) order;
 storage, that is the way of storing the objects of the container;
 traversal, that is the way of traversing the objects of the container.
Container classes are expected to implement methods to do the following:
 create an empty container (constructor);
 insert objects into the container;
 delete objects from the container;
 delete all the objects in the container (clear);
 access the objects in the container;
 access the number of objects in the container (count).
https://en.wikipedia.org/wiki/Container_(disambiguation)
 Container (abstract data type), a class or data structure that is a collection of other objects
 Container (type theory), abstractions that represent collection types in a uniform way
 Container (virtualization), a server virtualization method
 Container file format for storing related data together, such as audio and video data
https://en.wikipedia.org/wiki/Container_(abstract_data_type)
URL
https://en.wikipedia.org/wiki/Container_(abstract_data_type)

Venn diagrams and dimensionality
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We want to connect the construction of meaning and "making a point" to interpretation and representation by Venn diagrams  such that "the point" that that we are arguing is defined as (contained within) an "ndimensional envelope" can be fully represented by the overlap of Venn diagrams. Is that really feasible?
I'll have to explore that one facet at a time, but it looks promising.








