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The modern subject of topology studies space in a different way than geometry does. The geometric concepts of straightness, distance, and angle are excluded from topology, but the concept of boundary is central to topology. In topology, a sphere remains a sphere even when it's squeezed or stretched.
Not everything has a boundary. For instance, the circumference of a circle has no boundary. Also a spherical surface has no boundary. examples on math tutoring ; In topology, a finite region with no boundary is called a cycle. Circles and spherical surfaces are cycles. In general, if something is a boundary, it has no boundary itself. So boundaries are cycles. But not all cycles are boundaries.
Topology uses observation to distinguish various spaces. For instance, on a spherical surface, every circle is the boundary of a region on that surface. But on a toroidal surface (rotate a circle around a line in the plane of the circle that doesn't meet the circle), there are circles (for instance, that circle mentioned parenthetically) that don't bound any region on the surface. Thus, spherical surfaces are topologically different from toroidal surfaces. learn more on math forum.
The modern subject of topology studies space in a different way than geometry does. The geometric concepts of straightness, distance, and angle are excluded from topology, but the concept of boundary is central to topology. In topology, a sphere remains a sphere even when it's squeezed or stretched.
Not everything has a boundary. For instance, the circumference of a circle has no boundary. Also a spherical surface has no boundary. examples on math tutoring ; In topology, a finite region with no boundary is called a cycle. Circles and spherical surfaces are cycles. In general, if something is a boundary, it has no boundary itself. So boundaries are cycles. But not all cycles are boundaries.
Topology uses observation to distinguish various spaces. For instance, on a spherical surface, every circle is the boundary of a region on that surface. But on a toroidal surface (rotate a circle around a line in the plane of the circle that doesn't meet the circle), there are circles (for instance, that circle mentioned parenthetically) that don't bound any region on the surface. Thus, spherical surfaces are topologically different from toroidal surfaces. learn more on math forum.
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