$\sigma$-hereditarily closure-preserving $k$-networks and $g$-metrizability

SPACES WITH σ-WEAKLY HEREDITARILY CLOSURE-PRESERVING sn-NETWORKS

We prove that a space with a σ-weakly hereditarily closurepreserving sn-network is sn-first countable. As an application of this result, we prove that a Lindelöf space with a σ-weakly hereditarily closurepreserving sn-network is sn-second countable. The above results answer some questions posed by L. Yan. AMS Mathematics Subject Classification (2000): 54D20, 54D65, 54E20, 54E99

Weight and metrizability of inverses under hereditarily irreducible mappings

The main purpose of this paper is to study the weight under hereditarily irreducible mappings between continua. The main result states that if f : X → Y is an hereditarily irreducible and surjective mapping of a D-continuum X, then w(X) = w(Y ).

Closure Relation of K Orbits on G/B

Geometric Characterization of Hereditarily Bijective Boolean Networks

The study of relationships between structure and dynamics of asynchronous Boolean networks has recently led to the introduction of hereditarily bijective maps and even or odd self-dual networks. We show here that these two notions can be simply characterized geometrically: through orthogonality between certain affine subspaces. We also use this characterization to provide a construction of the ...

Alternative sigma factors F, E, G, and K in Clostridium botulinum sporulation and stress response

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