Class SpaceProperty

Overview

SpaceProperty is derived from the Space class and adds functionality to determine if the space has certain properties such as being compact, connected, or Hausdorff. These properties are crucial for determining if two spaces are homeomorphic.

Constructors

• Inherits Space constructor.

Member Functions

• bool isCompact(): Checks if the space is compact within \mathbb{R}.
• bool isConnected(): Checks if the space is connected.
• bool isHausdorff(): Checks if the space is Hausdorff.

Note: The current implementation assumes that the spaces are subsets of \mathbb{R}, where all sets are Hausdorff. Therefore, isHausdorff always returns true.

Example Usage

#include "homeomorphism.hpp"
 
// Assume space1 defined as before (see SpaceClass.mdx for reference)
topology::SpaceProperty space1Property(points, openSets);
 
// Check if space1 is compact and connected
bool isCompact1 = space1Property.isCompact();
bool isConnected1 = space1Property.isConnected();