Spacebook is a searchable database of topological spaces and their properties (in ZFC) inspired by Steen and Seebach’s *Counterexamples in Topology*.

(Learn more.)

(hover over property name for reference)

The selected space (**Uncountable Cartesian Product of Unit Interval**) is:

- Arcwise Connected
- Cardinality Not Exceeding Power Set of Continuum
- Compact
- Completely Regular
- Connected
- Countable Chain Condition
- Countably Compact
- Countably Metacompact
- Countably Paracompact
- Fully Normal
- Fully T4
- Lindelof
- Locally Arcwise Connected
- Locally Compact
- Locally Connected
- Locally Pathwise Connected
- Metacompact
- Normal
- Paracompact
- Pathwise Connected
- Pseudocompact
- Regular
- Second Category
- Semiregular
- Separable
- Sigma Compact
- Sigma Locally Compact
- Strong Locally Compact
- T0
- T1
- T2
- T2.5
- T3
- T3.5
- T4
- Urysohn
- Weakly Countably Compact

The selected space (**Uncountable Cartesian Product of Unit Interval**) is not:

- Biconnected
- Cardinality Equal Continuum
- Cardinality Less Than Continuum
- Completely Normal
- Countable
- Discrete
- Extremally Disconnected
- First Countable
- Has Dispersion Point
- Hyperconnected
- Metrizable
- Perfectly Normal
- Scattered
- Second Countable
- Sequentially Compact
- Sigma Locally Finite Base
- Strongly Connected
- T5
- Totally Disconnected
- Totally Path Disconnected
- Totally Separated
- Ultraconnected
- Zero Dimensional

It is unknown whether the selected space (**Uncountable Cartesian Product of Unit Interval**) is:

- No Properties Found