Closed Set

There are several equivalent definitions of a closed Set. A Set is closed if

1. The Complement of is an Open Set,

2. is its own Closure,

3. Sequences/nets/filters in which converge do so within ,

4. Every point outside has a Neighborhood disjoint from .

The Point-Set Topological definition of a closed set is a set which contains all ofits Limit Points. Therefore, a closed set is one for which, whatever point ispicked outside of , can always be isolated in some Open Set which doesn't touch .

• Sexagesimal
• Sexdecillion
• Sextic Equation
• Sextic Surface
• Sextillion
• Sexy Primes
• Seydewitz's Theorem
• Sgn
• Shadow
• Shadowing Theorem
• Shafarevich Conjecture
• Shah Function
• Shah-Wilson Constant
• Shallit Constant
• Shallow Diagonal
• Shanks' Algorithm
• Shanks' Conjecture
• Shannon Entropy
• Shannon Sampling Theorem
• Shape Operator
• Shapiro's Cyclic Sum Constant
• Sharing Problem
• Sharkovsky's Theorem
• Sharpe Ratio
• Sharpe's Differential Equation