Category:Characterization of Paracompactness in T3 Space

This category contains pages concerning Characterization of Paracompactness in T3 Space:

Let $T = \struct {X, \tau}$ be a $T_3$ space.

The following statements are equivalent:

$(1): \quad T$ is paracompact

$(2): \quad$ every open cover of $T$ has a locally finite refinement

$(3): \quad$ every open cover of $T$ has a closed locally finite refinement

$(4): \quad$ every open cover of $T$ is even

$(5): \quad$ every open cover of $T$ has an open $\sigma$-discrete refinement

$(6): \quad$ every open cover of $T$ has an open $\sigma$-locally finite refinement