## A Class of Translation Lattice |

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algebra of continuous Banach algebra Banach subalgebra base the sets bounded function bounded real-valued functions Bourbaki Class of Translation closed and closed closed equivalence relation closed under addition closed under continuous closed under multiplication closed under positive commutative diagram compact space completely regular space containing the constants continuous composition continuous functions continuous real-valued functions Corollary countable at infinity CZ(f discrete topology embedding f e L(A f e s f is continuous function f Hence home omorphism implies Isbell J. C. Taylor L(S+ latt lattice of functions locally compact multiplication by real obvious orem PENNSYLVANIA STATE UNIVERSITY positive inversion product topology Q-space R-valued functions real numbers result follows ring of quotients sat is fies satisfies L1 set of real-valued ſº sublattice subset theorem translation lattice containing translation lattice homomorphism uniformly closed valued extension weak topology defined