(τ-σ) paracompact with respect to ρ

Definition

• Let X be a set with three topologies τ, σ, and ρ. X is said to be (τ −σ) paracompact with respect to ρ if every τ-open cover of X has a σ-open refinement which is locally finite with respect to the topology ρ.

Remark

• τ1 paracompact with respect to τ2と違うことに注意

Reference

• Kovár, Martin M.,A note on the comparison of topologies.,Int. J. Math. Math. Sci. 26 (2001), no. 4, 233–237.